Advanced Placement (AP) Middle School

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!!

Answers

Answer 1

Answer:

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

Explanation:

:)

Answer 2

Answer:

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

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