question\nfactor.\n$x^2 + 2x - 24$
question\nfactor.\n$x^2 + 2x - 24$
Answer
Explanation:
Step1: Find two numbers
We need two numbers that multiply to (-24) (the constant term) and add up to (2) (the coefficient of (x)). Let's list the factor pairs of (-24): ((-1, 24)), ((1, -24)), ((-2, 12)), ((2, -12)), ((-3, 8)), ((3, -8)), ((-4, 6)), ((4, -6)). Among these, (-4) and (6) multiply to (-24) ((-4\times6 = -24)) and add up to (2) ((-4 + 6 = 2)).
Step2: Factor the quadratic
Using the two numbers we found, we can factor the quadratic (x^{2}+2x - 24) as ((x - 4)(x + 6)) (because when we expand ((x - 4)(x + 6)), we get (x^{2}+6x - 4x - 24=x^{2}+2x - 24), which matches the original expression).
Answer:
((x - 4)(x + 6))