CPM Homework Help : A2C Problem 9-9

Polynomials are expressions that can be written as a sum of terms of the form:
$(\text{any number}). x ^{(\text{whole number})}$

Which of the following equations are polynomial equations? For those that are not polynomials, explain why not. Check the lesson 9.1.1 Math Notes box for further details about polynomials.

$f\left(x\right) = 8x^{5} + x^{2} + 6.5x^{4} + 6$
Answer (a):
This is a polynomial.

$y = \frac { 3 } { 5 } x ^ { 6 } + 19 x ^ { 2 }$
Answer (b):
This is a polynomial.

$y = 2^{x} + 8$
Answer (c):
This is not a polynomial.

$f ( x ) = 9 + \sqrt { x } - 3$
Answer (d):
This is not a polynomial.

$P\left(x\right) = 7\left(x − 3\right)\left(x + 5\right)^{2}$
Answer (e):
This is a polynomial.

$y = x ^ { 2 } + \frac { 1 } { x ^ { 2 } + 5 }$
Answer (f):
This is not a polynomial.

Write an equation for a new polynomial function and then write an equation for a new function that is not a polynomial.
Hint (g):
Look at parts (a) through (f) for examples.