Question

What is the remainder when x3 - 1 is divided by (x + 2)?

Answer 1

Given:

The polynomial $x^3-1$ is divided by (x+2).

To find:

The remainder.

Solution:

Remainder theorem: If a polynomial p(x) is divided by (x-c), then the remainder is p(c).

Consider the polynomial:

$p(x)=x^3-1$

It is divided by (x+2). So, by the remainder theorem the remainder is p(-2).

Substituting x=-2 in the above polynomial, we get

$p(-2)=(-2)^3-1$

$p(-2)=-8-1$

$p(-2)=-9$

Therefore, the remainder is -9.