Chapter 8.8, Problem 13P

Factor each expression.

$21x^3+6x^2-28x-8$

To determine

To find: The factorization of $21x^3+6x^2-28x-8$

Answer to Problem 13P

  $(3x^2-4)(7x+2)$

Explanation of Solution

Given information: $21x^3+6x^2-28x-8$

Calculation:

  $\begin{array}{l}21x^3+6x^2-28x-8\\ =(21x^3+6x^2)-(28x+8)\\ =3x^2(7x+2)-4(7x+2)\\ =(3x^2-4)(7x+2)\end{array}$

Thus, $21x^3+6x^2-28x-8=(3x^2-4)(7x+2)$