Question

Find the remainder when p(x)= x^5 + x^4 + x^3 + x^2 + 2x + 2 is divided by q(x) = x + 1

Answer 1

0

Explanation:

Given a polynomial p(x) divided by (x + h), then the remainder is

p(- h)

Here divisor is (x + 1), so evaluate p(- 1) for remainder

p(- 1) =
`(-1)^(5)` +
`(-1)^(4)` + (- 1)³ + (- 1)² + 2(- 1) + 2

= - 1 + 1 - 1 + 1 - 2 + 2

= 0

This means that (x + 1) is a factor of p(x)