Chapter 4.6, Problem 1OE

To determine

To find which factorization is correct.

Answer to Problem 1OE

The correct factorization is, $x^2-8x-48=\left(x-12\right)\left(x+4\right)$

Explanation of Solution

Given information: The integer is, $x^2-8x-48$ .

Concept used: Factored completely.

A polynomial is factored completely when it is written as a product of factors and each factor is either a monomial, a prime polynomial, or a power of a prime polynomial.

Calculation: The required solution is obtained as,

  $\begin{array}{l}{x}^2-8x-48\\ =x^2-12x+4x-48\\ =x\left(x-12\right)+4\left(x-12\right)\\ =\left(x-12\right)\left(x+4\right)\end{array}$

The polynomial is factored completely since $\left(x-12\right)$ and $\left(x+4\right)$ .

Hence, the correct factorization is, $x^2-8x-48=\left(x-12\right)\left(x+4\right)$