Question

this is the only question in this section.
question
factor.
$x^2 + 2x - 15$
answer attempt 1 out of 10

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-15\) and add up to \(2\). Let's list the factor pairs of \(-15\): \((-1, 15)\), \((1, -15)\), \((-3, 5)\), \((3, -5)\). Among these, \(5\) and \(-3\) work because \(5\times(-3)=-15\) and \(5 + (-3)=2\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}+2x - 15\) as \((x + 5)(x - 3)\) because when we expand \((x + 5)(x - 3)\) using the distributive property (FOIL method), we get \(x^{2}-3x + 5x - 15=x^{2}+2x - 15\), which matches the original expression.

Answer:

\((x + 5)(x - 3)\)