Question

What is the remainder when x^{6}-4x^4+4x^2-10 is divided by x+3?

Answer 1

431

Explanation:

Let

`p(x) = {x}^(6) - 4 {x}^(4) + 4 {x}^(2) - 10`

We want to find the remainder when this polynomial is divided by x+3.

We use the remainder theorem.

Which says that, when p(x) is divided by x-a, the remainder is p(a)=R.

Therefore the remainder when p(x) is divided by x+3 is p(-3).

`p( - 3) = {( - 3)}^(6) - 4 { (- 3)}^(4) + 4 {( - 3)}^(2) - 10`

We evaluate:

`p( - 3) = 729 - 4 (81)+ 4 {( 9)} - 10`

We multiply to get;

`p( - 3) = 729 - 324+ 36- 10`

We simplify to get:

`p( - 3) =431`

Therefore the remainder is 431