Q 35 - Intermediate Algebra

Question

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

$3b(b-2)-13(b-2)$

Step-by-Step Solution

Answer

The given polynomial is factored as $3b(b-2)-13(b-2)=(b-2)(3b-13)$

Step 1. Given Information

Consider the polynomial $3b(b-2)-13(b-2)$.

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 $b-2$. And factoring the GCF we get 

$\begin{array}{rcl}3b(b-2)-13(b-2)& =& 3b·(b-2)-13·(b-2)\\ & =& (b-2)(3b-13)\end{array}$

Step 3. Check

Expanding the factors we get

$(b-2)(3b-13)=3b(b-2)-13(b-2)$

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