Answer
$5x^2-11+\frac{x+20}{x^2+2}$
Work Step by Step
We use the long division as be shown in the figure below.
Checking:
$$
(x^2+2)(5x^2-11)+x+20\\
=5x^4-11x^2+10x^2-22+x+20\\
=5x^4-x^2+x-2
$$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/dcd5a146-41bb-4d01-a343-8d5959495501/steps_image/small_1586347134.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000158Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=b62a49061c255ee2e3d74c3ccff9630052a5a148d8042c663163718bb44499fa)
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