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When p $(x) = x^{3}$ + ax + b is divided by $(x - 1)$ and by $(x + 1)$ , the remainders are 5 and 3 respectively. Find b.

Competition practiceAlgebra

A4
B0
C5
D2

Step-by-Step Solution

p (1) = 1 + a + b = 5

and

p (- 1) = - 1 - a + b = 3

. Adding:

2 b = 8

, so

b = 4

(and

a = 0

).

Answer: A) 4

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