Q. 255 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$4x^2+40x+84$

Step-by-Step Solution

Answer

The required factors are $4(x+3)(x+7)$

Step 1. Given Information

The given expression is $4x^2+40x+84$

Step 2. Calculation

We will find the factors by taking common factor out and then use the middle term splitting method.

$$\begin{gathered} 4x^2+40x+84=4(x^2+10x+21) \\ =4(x^2+7x+3x+21) \\ =4\left(x\right(x+7)+3(x+7\left)\right) \\ =4(x+3)(x+7) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 4(x+3)(x+7)=4\left(x\right(x+7)+3(x+7\left)\right) \\ =4(x^2+7x+3x+21) \\ =4(x^2+10x+21) \\ =4x^2+40x+84 \end{gathered}$$