Question

question
factor.
$x^2 + 2x - 24$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -24 (the constant term) and add up to 2 (the coefficient of the x term). Let's list the factor pairs of -24:

• 6 and -4: \(6\times(-4)= -24\) and \(6 + (-4)=2\)

Step2: Factor the quadratic

Using these two numbers, we can factor the quadratic \(x^{2}+2x - 24\) as \((x + 6)(x - 4)\) because when we expand \((x + 6)(x - 4)\), we get \(x^{2}-4x + 6x - 24=x^{2}+2x - 24\), which matches the original expression.

Answer:

\((x + 6)(x - 4)\)