Q 33 - Intermediate Algebra

Question

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

$5x(x+1)+3(x+1)$

Step-by-Step Solution

Answer

The given polynomial is factored as $5x(x+1)+3(x+1)=(x+1)(5x+3)$

Step 1. Given Information

Consider the polynomial $5x(x+1)+3(x+1)$.

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

$5x(x+1)+3(x+1)=(x+1)(5x+3)$

Step 3. Check

Expanding the factors we get

$(x+1)(5x+3)=5x(x+1)+3(x+1)$

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