Q 34 - Intermediate Algebra

Question

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

$2x(x-1)+9(x-1)$

Step-by-Step Solution

Answer

The given polynomial is factored as $2x(x-1)+9(x-1)=(x-1)(2x+9)$

Step 1. Given Information

Consider the polynomial $2x(x-1)+9(x-1)$.

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 $x-1$. And factoring the GCF we get

$\begin{array}{rcl}2x(x-1)+9(x-1)& =& 2x·(x-1)+9·(x-1)\\ & =& (x-1)(2x+9)\end{array}$

Step 3. Check

Expanding the factors we get 

$(x-1)(2x+9)=2x(x-1)+9(x-1)$

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