Chapter 8.5, Problem 33PPS

To determine

To factor: The polynomial $5g{f}^2+g^{2}f+15gf$

Answer to Problem 33PPS

  $gf\left(5f+g+15\right)$

Explanation of Solution

Given:

  $5g{f}^2+g^{2}f+15gf$

Calculation:

The Distributive Property is given by

  $a\left(b+c\right)=ab+ac\text{ and }ab+ac=a\left(b+c\right)$ , where a , b and c are real numbers

Now, in the given polynomial the GCF is $gf$

So, factored out the GCF and use the distributive property

  $\begin{array}{l}5g{f}^2+g^{2}f+15gf\\ =gf\left(5f+g+15\right)\end{array}$

So, the factored form is $gf\left(5f+g+15\right)$