Q. 352 - Intermediate Algebra

Question

In the following exercises, factor by grouping. 

$4x^2-16x+3x-12$

Step-by-Step Solution

Answer

The factored form of the polynomial is, 

$\left(x-4\right)\left(4x+3\right)$

Step 1. Given Information

We are given a polynomial,

$4x^2-16x+3x-12$

Step 2. Factorizing the polynomial

Grouping the terms, we get 

$4x^2-16x+3x-12=\left(4x^2-16x\right)+\left(3x-12\right)$

Factoring out greatest common factor, we get 

$4x^2-16x+3x-12=4x\left(x-4\right)+3\left(x-4\right)$

Now, again factoring out greatest common factor, we get  

$4x^2-16x+3x-12=\left(x-4\right)\left(4x+3\right)$

Step 3. Checking the factorization

 Multiplying the factors,  

$$\begin{gathered} \left(x-4\right)\left(4x+3\right)=4x^2-16x+3x-12 \\ x\left(4x+3\right)-4\left(4x+3\right)=4x^2-16x+3x-12 \\ 4x^2+3x-16x-12=4x^2-16x+3x-12 \\ 4x^2-16x+3x-12=4x^2-16x+3x-12 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.