Q. 37 - Intermediate Algebra

Question

Factor by Grouping In the following exercises, factor by grouping.

$a b+5 a+3 b+15$

Step-by-Step Solution

Answer

The simplest polynomial is $(b+5)(a+3)$

Step 1. Given

A polynomial is given as $a b+5 a+3 b+15$

Step 2. Concept Used

First we have to find the GCF (group common factor). Then we will factor out it after that we will group the given polynomial.

Step 3. Calculation

A polynomial is given as $a b+5 a+3 b+15$

First group the polynomial,

$a b+5 a+3 b+15=(a b+5 a)+(3 b+15)$

Factor out the GCF,

$$\begin{gathered} =a(b+5)+3(b+5) \\ =(b+5)(a+3) \end{gathered}$$

Step 4. Verification

Multiply the factors,

$(b+5)(a+3)=a b+3 b+5 a+15$