Question

question
factor.
$x^2 - 11x + 24$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(24\) (the constant term) and add up to \(-11\) (the coefficient of the middle term). Let's list the factor pairs of \(24\): \((1,24)\), \((2,12)\), \((3,8)\), \((4,6)\). Since the product is positive and the sum is negative, both numbers should be negative. Checking the pairs: \(-3\) and \(-8\) multiply to \(24\) (\((-3)\times(-8)=24\)) and add up to \(-11\) (\((-3)+(-8)=-11\)).

Step2: Factor the quadratic

Using the two numbers we found, we can factor the quadratic \(x^{2}-11x + 24\) as \((x - 3)(x - 8)\) because when we expand \((x - 3)(x - 8)\) using the distributive property (FOIL method), we get \(x^{2}-8x-3x + 24=x^{2}-11x + 24\), which matches the original quadratic.

Answer:

\((x - 3)(x - 8)\)