Chapter 8.6, Problem 18PPE

To determine

To calculate: The factor of $4w^2-5w-6$

Answer to Problem 18PPE

  $(4w+3)(w-2)$

Explanation of Solution

Given information: The expression $4w^2-5w-6$

Calculation:

  $\begin{array}{l}4w^2-5w-6\\ =4w^2-(8-3)w-6[24=8\times 3\text{and }5=8-3]\\ =4w^2-8w+3w-6\\ =(4w^2-8w)+(3w-6)\\ =4w(w-2)+3(w-2)[\text{factoring out the GCF from each of the two terms]}\\ =(4w+3)(w-2)[\text{factoring out the common factor }(w-2)]\end{array}$

Thus, $4w^2-5w-6=(4w+3)(w-2)$