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Tamamını benim çözeceğim konu özetle Ankara Ayt Tyt Deneme kampı 2 Mayıs’ta başlıyor kayıt ve bilgi için: 0 (505) 533 17 84 İzmir Ayt Matematik kampı...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/467755/8ec90ba16b4e4fa6642f883f6b9a075f/564x318_1"},"target":"_self","position":"0","reqid":"1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=videoid:16498201196395521378","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik öğretmeni Mustafa Güler tarafından sunulan TYT matematik serisinin ilk bölümüdür. Öğretmen, tahtada sorular çözerken öğrencilere adım adım çözüm yöntemlerini göstermektedir.","Videoda sayı kümeleri (rakamlar, sayma sayıları, doğal sayılar, tam sayılar, rasyonel sayılar, irrasyonel sayılar, reel sayılar), pozitif ve negatif sayılar, tek ve çift sayılar, ardışık sayılar, asal sayılar ve faktöriyel konuları ele alınmaktadır. Öğretmen, bu kavramları açıkladıktan sonra 2019-2024 yılları arasındaki TYT sınavlarından örnek sorular çözmektedir.","Video, TYT sınavına hazırlanan öğrenciler için temel matematik kavramlarını pekiştirmek ve sınav hazırlığı için hangi soruları çözmeleri gerektiğini göstermek amacıyla hazırlanmıştır. Öğretmen, ÖSYM'nin geçmiş yıllarda tekrar ettiği soru tiplerini göstererek, öğrencilerin dikkat etmesi gereken noktaları vurgulamaktadır."]},"endTime":2282,"title":"TYT Matematik Temel Kavramlar Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"TYT Matematik Temel Kavramlar Serisi","list":{"type":"unordered","items":["Matematik öğretmeni Mustafa Güler, TYT matematik serisinin ilk videosu olan temel kavramlar videosunu sunuyor.","Videoda sayı kümeleri, pozitif negatif sayılar, tek çift sayılar, ardışık sayılar, asal sayılar ve faktöriyel konuları ele alınacak.","Son 4-5 yıldan gelen benzer sorular çözülecek."]},"beginTime":0,"endTime":82,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=0&ask_summarization=1"},{"index":1,"title":"Sayı Kümeleri","list":{"type":"unordered","items":["Rakamlar 0'dan 9'a kadar olan sayılardır, sayma sayıları 1'den sonsuza kadar gider, doğal sayılar sayma sayılara 0'ı ekleyerek oluşur.","Tam sayılar eksi sonsuzdan artı sonsuza kadar gider, negatif tam sayılar Z harfi ile gösterilir, pozitif tam sayılar da Z harfi ile gösterilir.","Rasyonel sayılar a/b formunda gösterilen, b sıfırdan farklı gerçek sayılardır; irrasyonel sayılar ise virgülden sonrası belli olmayan düzensiz sayılardır."]},"beginTime":82,"endTime":179,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=82&ask_summarization=1"},{"index":2,"title":"Reel Sayılar ve Pozitif/Negatif Sayılar","list":{"type":"unordered","items":["Reel sayılar (gerçek sayılar), rasyonel ile irrasyonel sayıların birleşimidir ve tüm sayı kümesini kapsar.","Pozitif sayılar sıfırdan büyük, negatif sayılar sıfırdan küçük olan sayılardır.","Aynı cins sayıların çarpımı daima pozitiftir, zıt işaretli sayıların çarpımı daima negatiftir."]},"beginTime":179,"endTime":294,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=179&ask_summarization=1"},{"index":3,"title":"Tek ve Çift Sayılar","list":{"type":"unordered","items":["Tek sayılar 1, 3, 5, 7 gibi pozitif ve negatif sayılardır, çift sayılar 2, 4, 6, 8 gibi pozitif ve negatif sayılardır.","Aynı cins sayıların toplamı veya farkı daima tektir, farklı cins sayıların toplamı veya farkı daima çifttir.","Çarpmada birisi çift ise sonuç daima çifttir, çarpımları tekse her biri tektir, çarpımları çiftse en az biri çifttir."]},"beginTime":294,"endTime":430,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=294&ask_summarization=1"},{"index":4,"title":"Üslü Sayılar ve Örnek Sorular","list":{"type":"unordered","items":["Tek sayının pozitif tam sayı kuvveti daima tektir, çift sayının pozitif tam sayı kuvveti daima çifttir.","2024 TYT sınav sorusunda rasyonel olmayan bir gerçel sayı olarak √45 seçilmiştir.","Diğer bir soruda eşit bölmelere ayrılmış çubuklardan hangisinin 30 birim gösterdiği sorulmuştur."]},"beginTime":430,"endTime":636,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=430&ask_summarization=1"},{"index":5,"title":"Matematik Soruları Çözümü","list":{"type":"unordered","items":["Eğitmen, 2024 sınav sorularını ele alıyor ve özellikle sağ alttaki soruyu beğeniyor.","İlk soruda a ve b birer tam sayı olmak üzere, 3a+b, 4a-b, a+7b ifadelerinin ikisinin çift, birinin tek olduğu belirtiliyor.","İkinci soruda 2, 3, 4, 5, 6, 7, 8, 9 sayılarının bölünmeleri, toplamları ve çarpımları kullanılarak a'nın değeri bulunuyor."]},"beginTime":637,"endTime":793,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=637&ask_summarization=1"},{"index":6,"title":"Soru Çözümü Detayları","list":{"type":"unordered","items":["İlk soruda a ve b'nin her ikisinin de çift olması imkansız olduğu, çünkü bu durumda tüm ifadeler çift olur.","a çift ve b tek, a tek ve b çift durumları inceleniyor, ancak her ikisi de \"iki çift bir tek\" koşulunu sağlamıyor.","a tek ve b tek durumunda tüm ifadeler çift olduğu için, \"hangisi kesinlikle çifttir\" sorusuna cevap olarak a+b toplamı bulunuyor."]},"beginTime":793,"endTime":978,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=793&ask_summarization=1"},{"index":7,"title":"İkinci Soru Çözümü","list":{"type":"unordered","items":["İkinci soruda bölümlerin 4'ü veren sayılar 8 ve 2 olarak belirleniyor.","Toplamların 7'yi veren sayılar 3 ve 4, farkların 4'ü veren sayılar 9 ve 5 olarak bulunuyor.","Kalan tek sayı 6 ve 7 olarak belirleniyor, çarpımları 42 olarak hesaplanıyor."]},"beginTime":978,"endTime":1047,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=978&ask_summarization=1"},{"index":8,"title":"Üçüncü Soru Çözümü","list":{"type":"unordered","items":["Üçüncü soruda b+c ifadesinin her zaman tek olduğu belirtiliyor.","a-b-c ifadesinin çift olduğu, çünkü b+c tek olduğunda çarpım durumunda her iki sayı da çift olur.","Sonuç olarak a, b ve c'nin hepsinin çift olduğu sonucuna varılıyor."]},"beginTime":1047,"endTime":1148,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1047&ask_summarization=1"},{"index":9,"title":"Ardışık Sayılar","list":{"type":"unordered","items":["Ardışık tam sayılar birer birer artar: x, x+1, x+2, x+3 şeklinde devam eder.","Ardışık çift sayılar ikişer ikişer artar: x, x+2, x+4, x+6 şeklinde devam eder.","Ardışık tek sayılar ikişer ikişer artar: 1, 3, 5, 7 şeklinde devam eder.","Ardışık sayılarda üçer üçer artan ve üçün katından bir fazla olan sayılar için toplam formülü: ortanca çarpı terim sayısıdır."]},"beginTime":1157,"endTime":1279,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1157&ask_summarization=1"},{"index":10,"title":"Asal Sayılar","list":{"type":"unordered","items":["Asal sayılar, bir ve kendisinden başka ortak böleni olmayan bir'den büyük tam sayılardır.","En küçük asal sayı iki'dir.","6, 8, 51, 91 gibi sayılar asal değildir çünkü rakamları toplamı için katsayıları vardır."]},"beginTime":1279,"endTime":1327,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1279&ask_summarization=1"},{"index":11,"title":"Faktöriyel Kavramı","list":{"type":"unordered","items":["Faktöriyel, bir sayıdan başlayıp azalarak bir'e kadar sayıların çarpımıdır.","n faktöriyel, n'den başlayıp n-1, n-2 azalarak bir'e kadar sayıların çarpımıdır.","0 şeklinde faktöriyel 1'e eşittir, 1 faktöriyel de 1'e eşittir."]},"beginTime":1327,"endTime":1409,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1327&ask_summarization=1"},{"index":12,"title":"Faktöriyel Sorusu","list":{"type":"unordered","items":["2021 benzer sınav sorusunda, dokuz ülkede on iki şehirde her katında beş odalı iki katlı on bir hastane yapılacağı belirtilmiştir.","Toplam oda sayısı 9×10×11×12 şeklinde hesaplanmıştır.","Bu ifade 12! - 8! şeklinde yazılabilir ve 9×10×11×12 sonucuna ulaşılır."]},"beginTime":1409,"endTime":1541,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1409&ask_summarization=1"},{"index":13,"title":"Rakam Sorusu","list":{"type":"unordered","items":["Bir a sayısında bulunan farklı rakamların sayısı daire içerisinde gösterilmiştir.","x bir rakam olmak üzere, toplamları beş veren farklı rakamlar 2 ve 3'tür.","x'in değerleri çarpımı 7×1=7 olarak bulunmuştur."]},"beginTime":1541,"endTime":1695,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1541&ask_summarization=1"},{"index":14,"title":"Ardışık Çift Sayılar Sorusu","list":{"type":"unordered","items":["a, b, c ardışık çift sayılar olarak verilmiştir.","Ardışık çift sayılar ikişer ikişer artar.","a+b+c toplamı 15 olarak hesaplanmıştır."]},"beginTime":1695,"endTime":1756,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1695&ask_summarization=1"},{"index":15,"title":"2023-2024-2019 Sınav Soruları","list":{"type":"unordered","items":["ABC şehirlerin yerel saatleri arasındaki farklar inceleniyor; A ile B şehirleri arasındaki saat farkı 5 saat, B ile C şehirleri arasındaki saat farkı 3 saat.","C şehrinin hangi saat değerini alamayacağı hesaplanıyor; A şehri 15:00 iken, B şehri 18:00 veya 12:00, C şehri ise 15:03 veya 15:03 olabilir.","C şehrinin 15:00 olarak olamayacağı sonucuna varılıyor."]},"beginTime":1758,"endTime":1950,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1758&ask_summarization=1"},{"index":16,"title":"Teknik Çiftlik Sorusu","list":{"type":"unordered","items":["İçinde eşit sayıda isot bulunan iki çuval var; A sınıfına dağıtıldığında 4 isot artıyor, B sınıfına dağıtıldığında ise 1 öğrenci isot alamıyor.","A sınıfında x-4 öğrenci, B sınıfında x+1 öğrenci olduğu ve aralarındaki farkın 5 olduğu belirleniyor.","Sınıfların birinin tek, birinin çift olduğu sonucuna varılıyor; ancak her çuvalda çift sayıda isot olduğu iddiası yanlış bulunuyor."]},"beginTime":1950,"endTime":2108,"href":"/video/preview/16498201196395521378?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1950&ask_summarization=1"},{"index":17,"title":"2019 Sınav Sorusu","list":{"type":"unordered","items":["Ali 62'den başlayarak 7'şer 7'şer sayarak iki basamaklı bir sayı buluyor ve sonra geriye doğru 5'er 5'er sayarak 35'e ulaşıyor.","İki basamaklı sayı 5'in katı olduğu sonucuna varılıyor; 62'ye 28 eklenerek 90 sayısı bulunuyor.","A×B çarpımı 90 olarak 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Çözülen problemler arasında kar-zarar problemleri, otobüs garajı problemleri, matbaa baskı hataları ve sayfa numaralarının rakamları toplamı verildiğinde kitabın kaç sayfadan oluştuğunu bulma gibi farklı konular yer almaktadır.","Öğretmen, kitabın temel düzey, orta düzey ve yeni nesil problemler içerdiğini belirtmekte ve her soru için gerekli denklemleri kurarak ve hesaplamaları göstererek çözüm sürecini detaylı şekilde anlatmaktadır. Ayrıca, kitabın tüm sorularının çözümlerinin kendisinin yaptığını ve karekod üzerinden erişilebileceğini de belirtmektedir."]},"endTime":1486,"title":"Matematik Problemleri Kitabı Tanıtımı ve Soru Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Yeni Problemler Kitabı Tanıtımı","list":{"type":"unordered","items":["Konuşmacı, izleyicilerin isteği üzerine kendi kitabından problemler soruları çözeceğini belirtiyor.","Problemler kitabı geçen cuma günü (üç gün önce) çıktı ve Google'da \"matematiğin güler yüzlü problemler\" araması yapıldığında bulunabilir.","Kitap, doğrukaynak.com sitesinde şehirlerdeki kırtasiyelerde bulunabilir."]},"beginTime":2,"endTime":49,"href":"/video/preview/7366432552315966937?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=2&ask_summarization=1"},{"index":1,"title":"Kitabın Hazırlanma Süreci","list":{"type":"unordered","items":["Kitap, pandemi nedeniyle 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Öğretmen, tahtada notalar alarak konuyu adım adım açıklamaktadır.","Videoda polinomların bölünmesi, kalan bulma, çarpanlara ayırma, dereceleri ve kökleri gibi temel konular ele alınmaktadır. Öğretmen, çeşitli polinom sorularını çözerek \"x yerine bulunan değeri yazma\" tekniği, polinom bölmesi kalıbı (P(x) = B(x) * Q(x) + K(x)) ve kalanın derecesinin her zaman bölenin derecesinden küçük olması gibi önemli kuralları açıklamaktadır.","Video, 2023 AYT sınavında çıkan benzer soruların çözümüyle desteklenmekte ve öğrencilerin sık yaptığı hatalar hakkında uyarılar içermektedir. 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gördüğünüz yere 1 yazmanız yeterlidir, bu bir denklem çözme değil, TYT konusu değildir.","x²-4 ile tam bölünüyor demek, kalanın sıfır olduğunu gösterir ve x² gördüğünüz yere 4 yazmanız gerekir.","Polinom bölme sorularında, kalanı bulmak için x küp gördüğünüz yere 1 yazarak işlemi tamamlarsınız."]},"beginTime":739,"endTime":906,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=739&ask_summarization=1"},{"index":4,"title":"Tam Bölme Örneği","list":{"type":"unordered","items":["x⁴/x² tam bölünüyorsa kalan sıfırdır ve x² gördüğünüz yere 4 yazarsınız.","Tam bölme durumunda, kalan sıfır olduğundan x'in önündeki katsayıların toplamı sıfır olmalıdır.","Soruda x²+x+1/x+1 ile bölümünden kalanı bulmak için x² gördüğünüz yere x-1 yazmanız gerekir."]},"beginTime":906,"endTime":1212,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=906&ask_summarization=1"},{"index":5,"title":"Polinom Bölmesi Kalıbı","list":{"type":"unordered","items":["Polinom bölmesinde kalanı bulmak için x yerine bölme işlemindeki değeri (örneğin -1) yazarsınız.","Polinom bölmesinde bölüm polinomunun katsayıları toplamını bulmak için, kalanı denklemde karşıya atarak hesaplayabilirsiniz.","2023'deki benzer soruları çözmek için bu kalıbı uygulayabilirsiniz."]},"beginTime":1212,"endTime":1341,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1212&ask_summarization=1"},{"index":6,"title":"Polinomlar ve Kökler","list":{"type":"unordered","items":["Birinci soruda, katsayısı bir olan üçüncü dereceden P(x) ve R(x) polinomlarının iki ve altı ortak kökleri vardır.","P(x) polinomunun ekstra kökü m, R(x) polinomunun ekstra kökü n olarak belirlenmiştir.","P(x) - R(x) ifadesinin değeri 36 olarak bulunmuştur."]},"beginTime":1351,"endTime":1597,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1351&ask_summarization=1"},{"index":7,"title":"İkinci Dereceden Denklemler","list":{"type":"unordered","items":["İkinci dereceden denklemlerde reel köklerin varlığı delta (Δ) değerine bağlıdır: Δ\u003c0 ise reel kök yoktur, Δ>0 ise iki farklı reel kök vardır.","Δ formülü b²-4ac'tir.","Polinom soruları genellikle diğer konularla ilişkilendirilir: 2021'de eşitlik, 2022'de parabol ve ikinci dereceden denklemler soruları çıkmıştır."]},"beginTime":1597,"endTime":1900,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1597&ask_summarization=1"},{"index":8,"title":"Polinom Bölmesi","list":{"type":"unordered","items":["Bir polinomu x²'ye böldüğünüzde kalan ax+b şeklinde olur.","Polinom bölmesinin kalıbı: P(x) = (x²+4x+3)·B(x) + ax+b şeklinde kurulur.","P(-1) = -7 ve P(-3) = -13 değerleri kullanılarak a=3 ve b=-4 bulunur, kalan 3x-4 olarak hesaplanır."]},"beginTime":1900,"endTime":2128,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=1900&ask_summarization=1"},{"index":9,"title":"Polinom Çarpma Kuralları","list":{"type":"unordered","items":["Bir polinomu x ile çarptığınızda en küçük derece x olur, bu nedenle sabit sayı olmamalıdır.","Polinomu çarptığınızda en küçük dereceye sahip terim, çarpanın en küçük derecesi ile çarpımın en küçük derecesi olur.","Polinomlarda çarpanın derecesi, çarpımın içindeki en büyük üsün katları olmalıdır."]},"beginTime":2699,"endTime":2910,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=2699&ask_summarization=1"},{"index":10,"title":"Polinom Denklemleri Çözümü","list":{"type":"unordered","items":["Polinom denklemlerinde, polinom içindeki değişkenin yerine belirli bir değer yazarak denklem çözülebilir.","Polinomun sabit terimi, x yerine 0 yazarak bulunabilir.","Polinomun katsayıları toplamı, x yerine 1 yazarak bulunabilir."]},"beginTime":2910,"endTime":3060,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=2910&ask_summarization=1"},{"index":11,"title":"Kökler ve Dereceler","list":{"type":"unordered","items":["Bir polinomun derecesi, içindeki en büyük üs değerine eşittir.","Bir polinomun sadece iki farklı kökü varsa, üçüncü dereceden bir polinomda bu köklerin biri en az iki kez tekrarlanmalıdır.","Polinomun belirli bir değerindeki değeri, x yerine o değeri yazarak bulunabilir."]},"beginTime":3060,"endTime":3265,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=3060&ask_summarization=1"},{"index":12,"title":"Polinom Değişken Değiştirme","list":{"type":"unordered","items":["Polinomlarda değişken değiştirme yaparak, farklı değerler için polinomun değerini bulabilirsiniz.","Polinomun katsayıları, değişken değiştirme işleminden sonra bulunabilir.","Testlerde soruları çözerken, zorlanmadığınız sorulardan başlayabilirsiniz."]},"beginTime":3265,"endTime":3417,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=3265&ask_summarization=1"},{"index":13,"title":"Polinom Çarpanları ve Kökleri","list":{"type":"unordered","items":["P(x) polinomunun 3 bir kökü, ancak R(x) polinomunun kökü değil.","R(x) polinomunun tüm kökleri aynı zamanda P(x) polinomunun kökü olduğundan, P(x) = (x-3)·R(x) şeklinde ifade edilebilir.","P(x) polinomunun derecesi 3'tür ve x² katsayısı -5a, x katsayısı 3b-2x-3b olarak verilmiştir."]},"beginTime":3428,"endTime":3744,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=3428&ask_summarization=1"},{"index":14,"title":"Polinomların Dereceleri","list":{"type":"unordered","items":["Polinomların toplama ve çıkarma işlemi yapıldığında, derece büyük olan ifadenin derecesidir.","Çarpma işleminde dereceler toplanır, bölme işleminde ise çıkarılır.","Polinomun derecesi, en büyük üssü olan terimin üssüdür ve öndeki katsayıların değeri dereceyi etkilemez."]},"beginTime":3744,"endTime":3953,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=3744&ask_summarization=1"},{"index":15,"title":"Derece Problemi Çözümü","list":{"type":"unordered","items":["P(x) polinomunun derecesi 12'dir ve P(x)·Q(x)² = 30 olduğuna göre, Q(x) polinomunun derecesi 9'dur.","Bölme işleminde üstler çıkarıldığından, P(x)/Q(x) polinomunun derecesi 3'tür."]},"beginTime":3953,"endTime":4136,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=3953&ask_summarization=1"},{"index":16,"title":"Polinomların Dereceleri ve Çarpımları","list":{"type":"unordered","items":["Polinomların çarpımı sırasında dereceler toplanır ve bir polinomun derecesi diğerinin derecesinden bir fazla olmalıdır.","Verilen problemde, x²·px = x·rx eşitliğinde px'in derecesi 6, rx'in derecesi 7 olarak bulunmuştur.","p(rx) ifadesinde x yerine rx yazılarak sonuç 42 olarak hesaplanmıştır."]},"beginTime":4140,"endTime":4414,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=4140&ask_summarization=1"},{"index":17,"title":"Polinomlarda Bölme İşlemi","list":{"type":"unordered","items":["Polinomlarda bölme işlemi, bölünenin derecesi bölenin derecesinden büyük veya eşit olduğunda yapılır.","Kalanı bulmak için, bölenin sıfırı olan değeri bölünen polinomuna yerine yazılır.","Bölümü bulmak için polinom bölmesi yapılır ve bölüm ile bölenin çarpımı kalana eklenerek bölünen polinomu elde edilir."]},"beginTime":4414,"endTime":4503,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=4414&ask_summarization=1"},{"index":18,"title":"Polinom Bölmesi Örnekleri","list":{"type":"unordered","items":["Polinom bölmesi yaparken, en yüksek dereceli terimden başlayarak bölenle çarpım yapılır ve çıkarım işlemi uygulanır.","Örnek olarak 3x³+4x²+5x+2 ifadesi x-2'ye bölündüğünde bölüm 3x²+2x+9, kalan 20 olarak bulunmuştur.","Diğer bir örnekte x²+5x+2 ifadesi x+4'e bölündüğünde bölüm x+1, kalan -2 olarak hesaplanmıştır."]},"beginTime":4503,"endTime":4756,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=4503&ask_summarization=1"},{"index":19,"title":"Polinom Bölmesinin Özellikleri","list":{"type":"unordered","items":["Polinom bölmesinde kalın bir formül vardır: px = bx·qx + kx, burada px bölünen, bx bölen, qx bölüm ve kx kalanı temsil eder.","Kalanın derecesi her zaman bölenin derecesinden küçüktür.","Örneğin, bir polinom x²'ye bölündüğünde kalan ax+b veya sadece b şeklinde olabilir."]},"beginTime":4756,"endTime":4880,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=4756&ask_summarization=1"},{"index":20,"title":"Polinom Bölmesi Kalıbı","list":{"type":"unordered","items":["Öğrenciler polinom bölmesi konusunda kuyruğun koptuğu yerde sık sık hata yapıyorlar.","Eğer soruda kalan x ile verilmişse veya bölümden bahsediliyorsa, polinom bölmesi kalıbı kullanılmalıdır.","Polinom bölmesi kalıbı: P(x) = B(x) × Q(x) + K(x) şeklindedir, burada P(x) bölünen, B(x) bölen, Q(x) bölüm ve K(x) kalanı temsil eder."]},"beginTime":4884,"endTime":5012,"href":"/video/preview/3811095069643280918?parent-reqid=1765286593367548-12891484002700867155-balancer-l7leveler-kubr-yp-sas-132-BAL&text=Matemati%C4%9Fin+G%C3%BCler+Y%C3%BCz%C3%BC&t=4884&ask_summarization=1"},{"index":21,"title":"Polinom Bölmesi 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