Q 49E - Intermediate Algebra

Question

Factor by Grouping
In the following exercises, factor by grouping.

$2x^2- 14x - 5x + 35$

Step-by-Step Solution

Answer

The obtained factors for the expression $2x^2- 14x - 5x + 35$ by using the grouping method are $\left(x-7\right)\left(2x-5\right)$.

Step 1 Given expression is,

$2x^2- 14x - 5x + 35$.

The objective is, we need to find the factors for this expression by using the grouping method.

Step 2 First group the terms with the common factors.

$2x^2- 14x - 5x + 35=\left(2x^2- 14x\right) +\left(- 5x + 35\right)$

Next factor out the common factors.

$$\begin{gathered} 2x^2- 14x - 5x + 35=2x\left(x-7\right) -5\left(x-7\right) \\ =\left(x-7\right)\left(2x-5\right) \end{gathered}$$

The obtained factors are,$\left(x-7\right)\left(2x-5\right)$.

Step 3 Let us check the answer by multiplying the factors.

$$\begin{gathered} \left(x-7\right)\left(2x-5\right)=2x^2-5x-14x+35 \\ =2x^2-14x-5x+35 \end{gathered}$$

which is true.