Q 36 - Intermediate Algebra

Question

In the following exercises, factor the greatest common factor from each polynomial.   

$6m(m-5)-7(m-5)$

Step-by-Step Solution

Answer

The given polynomial is factored as $6m(m-5)-7(m-5)=(m-5)(6m-7)$

Step 1. Given Information

Consider the polynomial $6m(m-5)-7(m-5)$.

The objective is to factor the polynomial by factoring the greatest common factor. 

Step 2. Factor the GCF

The GCF of the terms of the given polynomial is $m-5$. And factoring the GCF we get

$\begin{array}{rcl}6m(m-5)-7(m-5)& =& 6m·(m-5)-7·(m-5)\\ & =& (m-5)(6m-7)\end{array}$

Step 3. Check

Expanding the factors we get

$(m-5)(6m-7)=6m(m-5)-7(m-5)$

And we get the given polynomial. So the factor is done correctly.