CPM Homework Help : CCA2 Problem 8-9

Polynomials are expressions that can be written as a sum of terms of the form:

(any number). x^{(whole number)}

Which of the following equations are polynomial equations? For those that are not polynomials, explain why not. Check the Lesson 8.1.1 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.

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

$y=2^x+8$
Answer (c):
This is not a polynomial because x is an exponent.

$f\left(x\right) = 9 + \sqrt{x} − 3$
Answer (d):
This is not a polynomial because the power of x is a fraction, not a whole number.

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

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

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.