Chapter 8.2, Problem 54HP

To determine

To write: a four term polynomial that can be factored and then factor the polynomial.

Answer to Problem 54HP

The factorized form of the polynomialis $\left(t-7\right)\left(3d-5\right)$ .

Explanation of Solution

Given information:

A four term polynomial.

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 a four term polynomial.

  $3dt-21d+35-5t$

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 $3d$ common from first two terms and $-5$ common from last two terms of the polynomial.

  $\begin{array}{c}3dt-21d+35-5t=3d\left(t-7\right)-5\left(t-7\right)\\ =\left(t-7\right)\left(3d-5\right)\end{array}$

Thus, the factorized form is $3dt-21d+35-5t=\left(t-7\right)\left(3d-5\right)$ .