Question

Please help!! I am very confused right now!

When divided by x - 1, the polynomial P(x) = x5 + 2x3 +Ax + B, where A and B are constants, the remainder is equal to 2. When P(x) is divided by x + 3, the remainder is equal -314. Find A and B.

Thank you in advance!!

Answer 1

a = 3, b = 8

Step-by-step 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

Answer 2

P(1) = 15 + 2(13) +A*(1) + B = 2 : remainder theorem

P(-3) = (-3)5 + 2(-3)3 +A*(-3) + B = -314

A = 4 and B = -5

Step-by-step explanation:

:)