Chapter 12.2, Problem 36STP

To determine

To find: the factor of the given equation as per the given option.

Answer to Problem 36STP

C. $\left(x+2\right)\left(x-8\right)$ .

Explanation of Solution

Given:

The given equation is $x^2-6x-16$ .

The given options are:

  $\left(x+2\right)\left(x+8\right)$

  $\left(x-2\right)\left(x+8\right)$

  $\left(x+2\right)\left(x-8\right)$

  $\left(x-2\right)\left(x-8\right)$

Calculation:

As the given equation is $x^2-6x-16$ .

  $4x^4-5x^2-6=0$ .

Now, find the factor of the equation. Therefore,

  $\begin{array}{l}{x}^2-6x-16\left\{\text{given equation}\right\}\\ x^2-8x+2x-16\left\{\text{expand the given equation}\right\}\\ x\left(x-8\right)+2\left(x-8\right)\left\{\text{use distributive law}\right\}\\ \left(x+2\right)\left(x-8\right)\left\{\text{factor the given equation}\right\}\end{array}$

Thus, factor formed of the given equation is $\left(x+2\right)\left(x-8\right)$

Hence the correct option is (C).