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

Hmm ok here's example, hopefully it will help.

\(\large f(x)=x^2+2x\) <-- Polynomial right? It has multiple.... "nom..ials" or whatever..
\(\large g(x)=x\) <-- Monomial!

Dividing a Polynomial by a Monomial,\[\large \frac{f(x)}{g(x)}\qquad =\qquad \frac{x^2+2x}{x}\]

Answer 2

Two ways to simplify this? Hmm I guess one method would be to use Polynomial Long Division.

Another method would be to simply split the problem into fractions like this, \[\large \frac{x^2+2x}{x} \qquad = \qquad \frac{x^2}{x}+\frac{2x}{x}\]And then simplify them individually.
I dunno if that's the two methods that your book would describe :O But whatev.