seeing structure in expressions common core - If f(x) and g(x) are two polynomials, is \frac{f(x)}{g(x)} a polynomial?

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what is a polynomial

STEP 2: Recall how to divide two monomials

Divide the two given polynomials

If f(x) = x^{4} and g(x) = x^{5} then

\frac{f(x)}{g(x)} = \frac{x^{4}}{x^{5}} = \frac{1}{x} which is not a polynomial since \frac{1}{x} = x^{-1}

Since a polynomial should not have any negative exponents, the answer is not a polynomial.

Skills to recall:

What are exponents

What are the rules of exponents