Question

What is the remainder when a^3 - 4 is divided by a+2?
a)0
b)-6
c)-2
d)-12

Answer 1

The remainder is -12. Choice d)

Explanation:

The Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).

We have the polynomial

`P(a)= a^3 - 4`

To evaluate the remainder when P is divided by a+2, we only have to find P(-2):

`P(-2)= (-2)^3 - 4`

`P(-2)= -8 - 4=-12`

The remainder is -12. Choice d)