Question

When the polynomial in P(x) is divided by (x + a), the remainder equals P(a).

A. True
B. False

Answer 1

false

Explanation:

Answer 2

According to Remainder Theorem for the polynomials, for every polynomial P(x) there exist such polynomials G(x) and R(x), that
`P(x)=(x\pm a)G(x)+R(x)`.

When the polynomial in P(x) is divided by (x + a), then there exist such polynomials G(x) and R(x), that P(x)=(x+a)G(x)+R(x). Note that for x=-a:

P(-a)=(-a+a)G(-a)+R(-a)=0·G(a)+R(-a)=R(-a).
This means that P(-a) is the remainder, not P(a).
Answer: correct choice is B.