Question

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.

Answer 1

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.