Question

find the remainder when x ^ 4 + 4x^ 8- 5x^2 - 6x + 7 is divided by x-1; x-2

Answer 1

Step-by-step explanation:

(i) Let p(x) = 4x3 – 5x2 + 6x – 2. The zero of (x – 1) is 1. When p(x) is divided by (x – 1) the remainder is p( 1). Now, p(1) = 4(1)3 – 5(1)2 + 6(1) – 2 = 4 – 5 + 6 – 2 = 3 ∴ The remainder is 3. (ii) Let p(x) = x – 7x – x + 6. The zero of x + 2 is -2. When p(x) is divided by x + 2, the remainder is p(-2). Now, p(-2) = (-2)3 – 7(-2)2 – (-2) + 6 = – 8 – 7(4) + 2 + 6 = – 8 – 28 + 2 + 6 = -28. ∴ The remainder is -28.Read more on Sarthaks.com - https://www.sarthaks.com/966888/find-the-remainder-using-remainder-theorem-when-4x-5x-6x-is-divided-by-ii-7x-6-is-divided-by-x

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