Q. 351 - Intermediate Algebra

Question

In the following exercises, factor by grouping. 

$x^2+7x-3x-21$

Step-by-Step Solution

Answer

The factored form of the polynomial is,  

$\left(x+7\right)\left(x-3\right)$

Step 1. Given Information

We are given a polynomial, 

$x^2+7x-3x-21$

Step 2. Factorizing the polynomial

Grouping the terms, we get 

$x^2+7x-3x-21=\left(x^2+7x\right)-\left(3x+21\right)$

Factoring out greatest common factor, we get 

$x^2+7x-3x-21=x\left(x+7\right)-3\left(x+7\right)$

Now, again factoring out greatest common factor, we get  

$x^2+7x-3x-21=\left(x+7\right)\left(x-3\right)$

Step 3. Checking the factorization

Multiplying the factors,

$$\begin{gathered} \left(x+7\right)\left(x-3\right)=x^2+7x-3x-21 \\ x\left(x-3\right)+7\left(x-3\right)=x^2+7x-3x-21 \\ {x}^2-3x+7x-21=x^2+7x-3x-21 \\ {x}^2+7x-3x-21=x^2+7x-3x-21 \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.