Question

Create a unique example of dividing a polynomial by a monomial and provide the simplified form. Explain, in complete sentences, the two ways used to simplify this expression and how you would check your quotient for accuracy.

Answer 1

\[\large \frac{x^2 + 2x +1}{x}\]

first way to solve this:
\[\large \frac{x^2}{x} + \frac{2x}{x} + \frac{1}{x}\]
\[\large \implies x + 2 + \frac 1x\]

second way to solve is by division
x + 2 + 1/x
________________
x | x^2 + 2x + 1
- x^2
-------------
2x
- 2x
---------
1