Question

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

Answer 1

Answer:

431

Step-by-step 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