Question

When the polynomial p(x) = x^3+ ax^2+ bx+ 3 is divided by x+3, the remainder is 9.

a. Given that p(1) = 1. find a and b
b. Find the remainder when p(x) is divided by x-4

Answer 1

a = 3, b = 8

Explanation:

Since x+3 is a factor, x=-3 is a root. => f(−3)=2(−3)3+a(−3)2−b(−3)+3=0

=> 9a+3b=51 => 3a+b=17 — (1)

x-2 leaves a reminder of 15 => f(2)=2(2)3+a(2)2−b(2)+3=15

=>4a−2b=−4=>2a−b=−2 —- (2)

Adding (1) & (2), 5a=15=>a=3

Substituting the value of a in (1), b=8