Question

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

Answer 1

Answer:

The remainder is -12. Choice d)

Step-by-step 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)