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- XL - XXL | Polinom Soru Çözümü | Kolaydan ZORA 🚀 #ayt #matematik konularından \"Polinom\" konusundan toplamda 5 adet kolaydan zora sıralanmış soru çözümü yapıyoruz. Small Medium Large...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1658505/5006205224f7e4434c28cea0765b8bc3/564x318_1"},"target":"_self","position":"9","reqid":"1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=videoid:9247744708211028376","teaser":[{"list":{"type":"unordered","items":["Bu video, SML Hoca tarafından sunulan bir matematik eğitim içeriğidir. Öğretmen, polinomlar konusunu detaylı bir şekilde anlatmaktadır.","Videoda polinomlar konusu üzerinden beş farklı soru çözülmektedir. Sorular kolaydan zora doğru SML, X, Large ve XXLarge biçiminde kategorize edilmiştir. İlk üç soru detaylı olarak çözülmekte, polinomların özellikleri, dereceleri ve katsayıları hakkında bilgiler verilmektedir.","Öğretmen, soruları çözerken yorum gücünün önemini vurgulamakta ve öğrencilerin formüllerin nereden geldiğini bilmelerinin gerekliliğini belirtmektedir. Video, ÖSYM sınavlarında çıkan polinom sorularının çözüm tekniklerini göstermek amacıyla hazırlanmış olup, farklı zorluk seviyelerinde örnek sorular sunarak öğrencilere kendi seviyelerini belirlemeleri için rehberlik etmektedir."]},"endTime":1121,"title":"Polinomlar Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Polinomlar Konusuna Giriş","list":{"type":"unordered","items":["SML Hoca, matematik YouTube kanalında polinomlar konusunu ele alıyor.","ÖSYM'nin polinom soruları öğrencilere zor gelir ve her sınavdan sonra sosyal medyada meşhur sorular olur.","Videoda beş soru çözülecek ve sorular kolaydan zora doğru SML, X, Large ve XXLarge biçiminde kategorize edilmiş."]},"beginTime":0,"endTime":59,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=0&ask_summarization=1"},{"index":1,"title":"Small Soru Çözümü","list":{"type":"unordered","items":["İlk soruda bir polinomda bilinmeyen n'in alabileceği tam sayı değerleri soruluyor.","Bir ifadenin polinom belirtebilmesi için değişkenlerinin katsayıları reel sayı, kuvvetleri doğal sayı olmak zorunda.","n'in alabileceği değerler -2'den 3'e kadar olup, toplam 6 farklı tam sayı değeri vardır."]},"beginTime":59,"endTime":170,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=59&ask_summarization=1"},{"index":2,"title":"Medium Soru Çözümü","list":{"type":"unordered","items":["İkinci soruda P(x) ve Q(x) polinomlarının dereceleri birbirine eşit ve m'ninci dereceden polinomlar verilmiş.","P(x) ve Q(x) polinomlarının toplamının derecesi, m ve n'nin toplamına eşit olabilir veya daha küçük olabilir.","Toplamın derecesi m ve n'den büyük olamaz çünkü dereceler aynı iken toplam daha büyük olamaz."]},"beginTime":170,"endTime":305,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=170&ask_summarization=1"},{"index":3,"title":"Large Soru Çözümü","list":{"type":"unordered","items":["Üçüncü soruda a, b, c, d reel sayılar olmak üzere ax³ + bx² + cx + d = (x² - 1)P(x) denklemi verilmiş.","x = 1 ve x = -1 değerleri denklemde yerine konularak a = -c ve b = -d eşitlikleri elde edilir.","b = c eşitliği hakkında yorum yapılamaz çünkü a ve c hakkında bilgi elde edilebilirken b ve d hakkında bilgi elde edilemez."]},"beginTime":305,"endTime":536,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=305&ask_summarization=1"},{"index":4,"title":"İkinci Dereceden Polinom Problemi","list":{"type":"unordered","items":["İkinci dereceden gerçel katsayılı P(x) polinomunun baş katsayısı 1'dir ve P(x) polinomunun x+2 ve x bölümünden kalanlar birbirine eşittir.","P(x) polinomunun x-2 ile bölümünden kalan, P(x) polinomunun sabit teriminin iki katıdır.","P(x) polinomunun katsayılar toplamı P(1) olarak hesaplanır."]},"beginTime":540,"endTime":634,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=540&ask_summarization=1"},{"index":5,"title":"Polinomun Çözümü","list":{"type":"unordered","items":["P(x) polinomu baş katsayısı 1 olduğu için x²+ax+b şeklinde yazılır.","P(-2)=P(0) eşitliği kullanılarak a=2 bulunur.","P(2)=2P(0) eşitliği kullanılarak b=8 bulunur ve P(x)=x²+2x+8 olarak elde edilir.","P(1) değeri 11 olarak hesaplanır."]},"beginTime":634,"endTime":733,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=634&ask_summarization=1"},{"index":6,"title":"Yorum Gücü ve Öneriler","list":{"type":"unordered","items":["Sorunun çözümünün zorluğu değil, yorum gücünün yüksek olması nedeniyle \"XXLarge\" olarak nitelendirilmiştir.","Yorum yeteneğini yükseltmek için bol miktarda kitap okumak, problem çözmek ve matematiksel terimlerle içli dışlı olmak gerekir.","11. sınıf öğrencilerine hangi formül ve kuralın nereden geldiğini bilerek çalışmaları tavsiye edilmektedir."]},"beginTime":733,"endTime":824,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=733&ask_summarization=1"},{"index":7,"title":"İkinci Polinom Problemi","list":{"type":"unordered","items":["İkinci dereceden P(x) polinomu her m gerçel sayısı için P(m)≤P(5) eşitsizliğini sağlamaktadır.","Parabolün kolları aşağı doğru olduğu için tepe noktası (5,P(5)) noktasıdır.","P(3)>P(-1), P(0)=P(10) ve P(n)=P(5) olduğunda n'nin tek değeri vardır."]},"beginTime":824,"endTime":1033,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=824&ask_summarization=1"},{"index":8,"title":"Öğrenme Stratejisi","list":{"type":"unordered","items":["Öğrenciler ücretsiz PDF'yi indirip önce kendileri çözmeye çalışabilirler.","Zorlandıkları soruları işaretleyip daha sonra çözümü izlemeleri önerilmektedir.","Zorluk seviyesi gitgide arttığı için hangi seviyede takıldıklarını görebilirler."]},"beginTime":1033,"endTime":1107,"href":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=1033&ask_summarization=1"}],"linkTemplate":"/video/preview/9247744708211028376?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"SML - 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Small Medium Large...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3531547/846af5cbf089bfb1d0aa29b53f9f0f4c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/lNjYQwIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=videoid:778807200131571534","teaser":[{"list":{"type":"unordered","items":["Bu video, SML Hoca tarafından SML Matematik YouTube kanalında sunulan bir matematik eğitim içeriğidir. Eğitmen, parabol konusundan beş farklı soruyu adım adım çözmektedir.","Videoda parabol konusundan beş farklı soru kolaydan zora doğru çözülmektedir. İlk olarak \"small\" seviyesindeki bir soru, ardından \"medium\", \"large\" ve \"XL\" seviyesindeki sorular ele alınmaktadır. Her soru için parabol denklemleri, kökler arasındaki mesafe formülü, tepe noktası ve üçgenin alanı gibi matematiksel kavramlar açıklanmaktadır.","Eğitmen, bu serinin SML, XL-XXL serisi olarak devam edeceğini belirtmektedir. 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ifadenin katsayısı sıfır olmalı, bu nedenle m²-1=0 denklemi çözülür ve m=-1 bulunur.","f(-1) hesaplanarak cevap -3 olarak bulunur."]},"beginTime":33,"endTime":175,"href":"/video/preview/778807200131571534?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=33&ask_summarization=1"},{"index":2,"title":"Medium Soru - Tepe Noktası ve Parabol Denklemi","list":{"type":"unordered","items":["Tepe noktası (2,3) olan ve (0,7) noktasından geçen bir parabolden bahsediliyor.","Tepe noktası ve bir noktadan geçen parabolün denklemi f(x)=a(x-r)²+k şeklinde yazılır.","(0,7) noktasından geçtiği bilgisiyle a=1 bulunur ve parabol denklemi f(x)=(x-2)²+3 olur.","f(1) ve f(3) değerleri hesaplanarak çarpımı 48 olarak 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bulunuyor.","Parabolün tepe noktası (-k, -k) olarak belirleniyor ve parabol orijinden geçtiği için f(0) = 0 denkleminden k = 1/2 bulunuyor.","Parabol denklemi f(x) = 2(x+1/2)² - 1/2 olarak hesaplanıyor ve f(5) değeri 60 olarak bulunuyor."]},"beginTime":491,"endTime":644,"href":"/video/preview/778807200131571534?parent-reqid=1769486595725019-10448569586139597667-balancer-l7leveler-kubr-yp-klg-296-BAL&text=XL+Locall+One&t=491&ask_summarization=1"},{"index":5,"title":"XL Sorusu Çözümü","list":{"type":"unordered","items":["a ve b gerçel sayı olmak üzere f(x) = x² + ax + b parabolünün tepe noktası (-4, k) olarak belirleniyor.","Tepe noktasının ordinatı k = -Δ/4a formülüyle hesaplanıyor ve Δ = 16 olarak bulunuyor.","Üçgenin alanı 2 × AB / 2 formülüyle hesaplanıyor ve AB = 4 birim olarak bulunuyor, böylece üçgenin alanı 8 birim kare olarak 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