Question

analyze the given quantity and express it as
$x^2 + 10x + 24 = $

Explanation:

Step1: Find two numbers

We need two numbers that multiply to 24 (the constant term) and add up to 10 (the coefficient of the \(x\)-term). Let's list the factor pairs of 24: (1, 24), (2, 12), (3, 8), (4, 6). Among these, 4 and 6 add up to 10.

Step2: Factor the quadratic

Using the numbers 4 and 6, we can factor the quadratic \(x^{2}+10x + 24\) as \((x + 4)(x + 6)\) because \((x + a)(x + b)=x^{2}+(a + b)x+ab\), and here \(a = 4\), \(b = 6\).

Answer:

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