Chapter 8.5, Problem 45P

Write the correct factored form for each expression.

$g^2-13gh+42h^2$

To determine

To write : the correct factored form of given expression.

Answer to Problem 45P

  $\left(g-7h\right)\left(g-6h\right)$

Explanation of Solution

Given expression: $g^2-13gh+42h^2$

Calculation:

We will split the midle term into two terms whose sum is $-13gh$ and product is $42g^2{h}^2$ .

Therefore, by splitting the middle term , we get

  $\begin{array}{l}{g}^2-13gh+42h^2\\ =g^2-7gh-6gh+42h^2\\ =\left(g^2-7gh\right)+\left(-6gh+42h^2\right)\\ =g\left(g-7h\right)-6h\left(g-7h\right)\\ =\left(g-7h\right)\left(g-6h\right)\end{array}$

Thus, factored form of given expression is $\left(g-7h\right)\left(g-6h\right)$ .