Remainder theorem | Factor theorem| Polynomials #3 | Class 9 Maths

➡️ Watch the entire playlist for Class 9 Maths Polynomials : https://www.youtube.com/playlist?list=PLph3YM7PV2E70YLHou9BNKrQpFoH770gO The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a). Factor theorem is used when factoring completely the polynomials. In this video we will cover: 1. Remainder theorem: Dividend = (Divisor × Quotient) + Remainder 2. Zero of a polynomial is a number c for which the value of the polynomial p(x) is 0. 3. Remainder theorem: general rule 4. Find the remainder obtained on dividing p(x) = x^3 + 1 by x + 1. 5. Find the remainder when x^4 + x^3 – 2x^2 + x + 1 is divided by x – 1. 6. Check whether the polynomial q(t) = 4t^3 + 4t^2 – t – 1 is a multiple of 2t + 1. 7. Factor theorem 8. If p(x) is a polynomial of degree n ᐳ 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x). 9. Exercise 2.3 polynomial Class 9 Maths 10. Check whether 7 + 3x is a factor of 3x^3 + 7x. 11. Factorization of polynomials (middle term splitting, factor theorem) 12. Factorise y^2 – 5y + 6 by using the Factor Theorem 13. Determine which of the following polynomials has (x + 1) a factor : (i) x^3 + x^2 + x + 1 (ii) x^4 + x^3 + x^2 + x + 1 (iii) x^4 + 3x^3 + 3x^2 + x + 1 (iv) (iv) x^3-x^2-(2-sqrt(2)) x + sqrt(2) 14. Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x^3 + x^2 – 2x – 1, g(x) = x + 1 (ii) p(x) = x^3 + 3x^2 + 3x + 1, g(x) = x + 2 (iii) p(x) = x^3 – 4x^2 + x + 6, g(x) = x – 3 15. Find the value of k, if x – 1 is a factor of p(x) in each of the following cases: (i) p(x) = x^2 + x + k (ii) p(x) = 2x^2 + kx +sqrt(2) (iii) p(x) = kx^2 – sqrt(2) x + 1 (iv) p(x) = kx^2 – 3x + k LearnoHub.com (formerly called ExamFear Education) is a Free Education platform with more than 6000 videos on Physics, Chemistry, Maths, Biology, English, Science experiments, tips & tricks and motivational videos for Classes 6 to 12. Learn for Free! ➡️ Website: http://www.learnohub.com ➡️ Facebook: https://bit.ly/LearnoHubFB ➡️ Instagram: https://bit.ly/LearnoHubInsta ➡️ Get Our Videos in Pendrives: Class 9 - https://bit.ly/LHPenDrive9 ➡️ Take_Online Test: https://www.examfear.com/test/Class-9/Maths/Polynomials.htm About the Teacher: Roshni Mukherjee, the Founder-Educator at LearnoHub has been building this free learning platform since 2011. She has been recognised as one of the 100 Women Achievers of India by the Ministry of Women & Child Development and felicitated by the President of India in 2016. Roshni has been invited by Google to speak at Global Education Symposium 2017 held at Google Headquarters, California. Limca Book of Records also recognised our work. ➡️Watch Roshni's Tedx Talk to know more about her journey: https://www.youtube.com/watch?v=v2sW_oOf6TY #LearnoHubMaths #CBSEClass9Maths #SabkoSamajhAayega Join us and let us together build this Free Learning Platform! We will surely ensure that you enjoy the real learning with us. Copyright © All rights reserved. LearnoHub | ExamFear Education