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Ex 2.4, 5 If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a. Let p(x) = x4 − 6x3 + 16x2 − 25x + 10 q(x) = x2 − 2x + k Let’s divide p(x) by q(x) x2 − 2x + k x4 − 6x3 + 16x2 − 25x + 10 Thus, Remainder = –9x + 2kx + 10 – 8k + k2 = (2k − 9) x + k2 − 8k + 10 According to question, Remainder = x + a ∴ (2k − 9) x + k2 − 8k + 10 = x + a Comparing Therefore, k = 5 and a = −5 2k − 9 = 1 2k = 10 k = 5 k2 − 8k + 10 = a Putting k = 5 (5)2 − 8 (5) + 10 = a a = 25 − 40 + 10 a = −5

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.