# Discuss the following situation by computation or proving. Make sure to show your complete solution. Give a polynomial division that has a quotient of x+5 and a remainder of -2.

Discuss the following situation by computation or proving. Make sure to show your complete solution.
Give a polynomial division that has a quotient of x+5 and a remainder of -2.
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Step 1
Given:
Give a polynomial division that has a quotient of x + 5 and a remainder of -2.
Step 2
Let the polynomial is:
$⇒{x}^{2}+10x+23$
Dividing above polynomial by x+5:
$\frac{x+5}{⇒x+5}\left({x}^{2}+10x+23\right)$
$±{x}^{2}+-5x$
$5x+23$
$±5x±25$
-2
So, ${x}^{2}+10x+23$, that has a quotient of x+5 and remainder of -2.