Chapter 6.2, Problem 7MRE

To determine

To calculate: The factors of the polynomial $xy+3y-4xz-12z$.

Answer to Problem 7MRE

The polynomial $xy+3y-4xz-12z$ is factored as $\left(x+3\right)\left(y-4z\right)$.

Explanation of Solution

Given information:

The polynomial $xy+3y-4xz-12z$.

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $xy+3y-4xz-12z$.

From the first and second term of the polynomial take y as a common factor.

  $xy+3y-4xz-12z=y\left(x+3\right)-4xz-12z$

From the third and fourth term take $-4z$ as a common factor.

  $\begin{array}{c}xy+3y-4xz-12z=y\left(x+3\right)-4xz-12z\\ =y\left(x+3\right)-4z\left(x+3\right)\end{array}$

Take out the common factor,

  $\begin{array}{c}xy+3y-4xz-12z=y\left(x+3\right)-4xz-12z\\ =y\left(x+3\right)-4z\left(x+3\right)\\ =\left(x+3\right)\left(y-4z\right)\end{array}$

Thus, thepolynomial $xy+3y-4xz-12z$ is factored as $\left(x+3\right)\left(y-4z\right)$.