Q. 354 - Intermediate Algebra

Question

In the following exercises, factor by grouping. 

$5x-5y-y+x$

Step-by-Step Solution

Answer

The factored form of the polynomial is,

$6(x-y)$

Step 1. Given Information

We are given a polynomial, 

$5x-5y-y+x$

Step 2. Factorizing the polynomial

The given polynomial can be written as,

$5x-5y-y+x=5x-5y+x-y$

Grouping the terms, we get 

$5x-5y-y+x=\left(5x-5y\right)+\left(x-y\right)$

Factoring out greatest common factor, we get 

$5x-5y-y+x=5\left(x-y\right)+1\left(x-y\right)$

Now, again factoring out greatest common factor, we get 

$$\begin{gathered} 5x-5y-y+x=\left(x-y\right)\left(5+1\right) \\ 5x-5y-y+x=6\left(x-y\right) \end{gathered}$$

Step 3. Checking the factorization

Multiplying the factors,   

$$\begin{gathered} 6\left(x-y\right)=5x-5y-y+x \\ 6x-6y=5x-5y-y+x \\ 5x-5y-y+x=5x-5y-y+x \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.