Chapter 8.6, Problem 5STP

For Exercises $1-5,$ choose the correct letter.

What is the factored form of $3x^2+21x-24?$

A. $3(x+8)(x-1)$

B. $3(x+6)(x+1)$

C. $3(x+5)(x-3)$

D. $3(x+7)(x-3)$

To determine

To choose : the correct factored form of given expression.

 A. $3\left(x+8\right)\left(x-1\right)$

 B. $3\left(x+6\right)\left(x+1\right)$

 C. $3\left(x+5\right)\left(x-3\right)$

 D. $3\left(x+7\right)\left(x-3\right)$

Answer to Problem 5STP

 A. $3\left(x+8\right)\left(x-1\right)$

Explanation of Solution

Given expression: $3x^2+21x-24$

Calculation:

Each term of the expression has common factor 3, so we can take factor 3 out of each gterm of the expression as follows.

  $3x^2+21x-24=3\left(x^2+7x-8\right)$

Now, we spit the middle term in the bracket into two terms whose sum is 7x and product is $-8x^2$ as follows.

  $\begin{array}{l}3x^2+21x-24=3\left(x^2+8x-x-8\right)\\ 3x^2+21x-24=3\left[\left(x^2+8x\right)+\left(-x-8\right)\right]\\ 3x^2+21x-24=3\left[x\left(x+8\right)-\left(x+8\right)\right]\\ 3x^2+21x-24=3\left(x+8\right)\left(x-1\right)\end{array}$

Thus, the factorized form of given expression is $3\left(x+8\right)\left(x-1\right)$ .