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:

\(\Rightarrow x^{2}+10x+23\)

Dividing above polynomial by x+5:

\(\frac{x+5}{\Rightarrow x+5}(x^{2}+10x+23)\)

\(\pm x^{2}+-5x\)

\(5x+23\)

\(\pm 5x\pm 25\)

-2

So, \(x^{2}+10x+23\), that has a quotient of x+5 and remainder of -2.

Given:

Give a polynomial division that has a quotient of x + 5 and a remainder of -2.

Step 2

Let the polynomial is:

\(\Rightarrow x^{2}+10x+23\)

Dividing above polynomial by x+5:

\(\frac{x+5}{\Rightarrow x+5}(x^{2}+10x+23)\)

\(\pm x^{2}+-5x\)

\(5x+23\)

\(\pm 5x\pm 25\)

-2

So, \(x^{2}+10x+23\), that has a quotient of x+5 and remainder of -2.