Chapter 8.2, Problem 57STP

To determine

To find: Onefactor of $6z^2-3z-2+4z$ .

Answer to Problem 57STP

One factor of $6z^2-3z-2+4z$ is $2z-1$ that is option D.

Explanation of Solution

Given information:

Given option

A. $2z+1$

B. $3z-2$

C. $z+2$

D. $2z-1$

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.

  $6z^2-3z-2+4z$

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

  $\begin{array}{c}6z^2-3z-2+4z=3z\left(2z-1\right)+2\left(2z-1\right)\\ =\left(3z+2\right)\left(2z-1\right)\end{array}$

Thus, the factorized form is $6z^2-3z-2+4z=\left(3z+2\right)\left(2z-1\right)$ .