Chapter 8.2, Problem 31PPS

To determine

To factor: The given polynomial.

Answer to Problem 31PPS

The factorized form of the polynomialis $\left(5b+2\right)\left(r-5\right)$ .

Explanation of Solution

Given information:

The polynomialis $5br-25b+2r-10$ .

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.

  $5br-25b+2r-10$

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 $5b$ common from first two terms and $2$ common from last two terms of the polynomial.

  $\begin{array}{c}5br-25b+2r-10=5b\left(r-5\right)+2\left(r-5\right)\\ =\left(5b+2\right)\left(r-5\right)\end{array}$

Thus, the factorized form is $5br-25b+2r-10=\left(5b+2\right)\left(r-5\right)$ .