Chapter 7.6, Problem 23E

To determine

To describe: Error to be described in factoring the given polynomial and to correct it.

Answer to Problem 23E

  $2$ is taken common from the polynomial $2x^2-2x-24$ in a wrong way.

Correct factorization is $2x^2-2x-24$

  $=2(x+3)(x-4)$ .

Explanation of Solution

Given information: $2x^2-2x-24=2(x^2-2x-24)$

  $=2(x-6)(x+4)$ , where ‘ $x$ ’ is a variable.

Calculation:$2$ must be taken common from each term of the polynomial, that is,

  $2x^2-2x-24=2(x^2-x-12)$ (Taking $2$ common)

  $=2(x^2-4x+3x-12)$

  $=2(x(x-4)+3(x-4))$

  $=2(x+3)(x-4)$

Thus, $2x^2-2x-24$

  $=2(x+3)(x-4)$ .