Question

Please please help!!!! I will give brainliest!!!!! Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Answer 1

Given:

$p(x)=2x^4+x^2-10x-1$ divided by $x+2$

To find:

The remainder.

Solution:

$p(x)=2x^4+x^2-10x-1$ divided by $x+2$

Remainder theorem:

If a polynomial p(x) is divide by x - a, then the remainder is p(a).

$x+2=0$

Subtract 2 from both sides, we get

$x=-2$

substitute x = -2 in p(x).

$p(-2)=2(-2)^4+(-2)^2-10(-2)-1$

          $=2(16)+(4)+20-1$

          $=32+4+19$

          $=55$

The remainder is 55.