Chapter 8.2, Problem 37PPS

To determine

To factor: The given polynomial.

Answer to Problem 37PPS

The factorized form of the polynomialis $\left(6t+4\right)\left(8u-15\right)$ .

Explanation of Solution

Given information:

The polynomialis $48tu-90t+32u-60$ .

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.

  $48tu-90t+32u-60$

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 $6t$ common from first two terms and $4$ common from last two terms of the polynomial.

  $\begin{array}{c}48tu-90t+32u-60=6t\left(8u-15\right)+4\left(8u-15\right)\\ =\left(6t+4\right)\left(8u-15\right)\end{array}$

Thus, the factorized form is $48tu-90t+32u-60=\left(6t+4\right)\left(8u-15\right)$ .