Problem 70 - Introductory Algebra for College Students

Question

Factor by grouping. $$x^{2}+3 x+5 x+15$$

Step-by-Step Solution

Answer

The factorized form of the expression is \((x + 3)(x + 5)\).

Step 1 - Group Terms

First, the polynomial needs to be grouped in a useful way. In this case, \(x^{2}+3 x\) & \(+5 x+15\) are grouped together.

Step 2 - Factor out from Each Grouping

From the first group \(x^{2}+3 x\), \(x\) can be factored out resulting in \(x(x +3)\). From the second group \(5 x+15\), \(5\) can be factored out resulting in \(5(x + 3)\).

Step 3 - Combine Common Terms

Since \(x + 3\) is common to both expressions, it can be factored. The resulting factorization is \((x + 3)(x + 5)\)