Q 50E - Intermediate Algebra

Question

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

$4x^2- 36x - 3x + 27$.

Step-by-Step Solution

Answer

The obtained factors for the expression $4x^2- 36x - 3x + 27$ by using the grouping method are, $\left(x-9\right)\left(4x-3\right)$.

Step 1 Given expression is,

$4x^2- 36x - 3x + 27$.

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.

$4x^2- 36x - 3x + 27=\left(4x^2- 36x\right)+\left(- 3x + 27\right)$

Now factor out the common factors.

$$\begin{gathered} 4x^2- 36x - 3x + 27=4x\left(x-9\right)-3\left(x-9\right) \\ =\left(4x-3\right)\left(x-9\right) \end{gathered}$$

The obtained factors are,$\left(x-9\right)\left(4x-3\right)$.

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

$$\begin{gathered} \left(x-9\right)\left(4x-3\right)=4x^2-3x-36x+27 \\ =4x^2-36x-3x+27 \end{gathered}$$

which is true.