Chapter 8.2, Problem 33PPS

To determine

To factor: The given polynomial.

Answer to Problem 33PPS

The factorized form of the polynomialis $gf\left(5f+g+15\right)$ .

Explanation of Solution

Given information:

The polynomialis $5g{f}^2+g^{2}f+15gf$ .

Formula used:

The distribution laws stated as multiply a number by groups of numbers having subtraction or addition operation between them same as multiplication done separately. That is,

  $\begin{array}{l}ab-ac-ad=a\left(b-c-d\right)\\ ab+ac+ad=a\left(b+c+d\right)\end{array}$

Concept used:

Factorized form of a polynomial is the product form of some binomial or trinomials or product of a constant and a polynomial.

Calculation:

Consider the given polynomial.

  $5g{f}^2+g^{2}f+15gf$

Recall that the distribution laws stated as multiply a number by groups of numbers having subtraction and addition operation between them same as multiplication done separately. That is,

  $ab-ac=a\left(b-c\right)$

Apply it and take $gf$ common from each term of the polynomial.

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

Thus, the factorized form is $5g{f}^2+g^{2}f+15gf=gf\left(5f+g+15\right)$ .