Questions: Factor. (If the expression is nonfactorable over the integers, enter NONFACTORABLE.) a^2-11 a+24

Transcript text: 10. [-/0.6 Points] DETAILS MY NOTES AUFINTERALG9 5.6.017. Factor. (If the expression is nonfactorable over the integers, enter NONFACTORABLE.) \[ a^{2}-11 a+24 \] $\square$ Need Help? Read It Submit Answer

Solution

Solution Steps

To factor the quadratic expression $a^2 - 11a + 24$, we need to find two numbers that multiply to the constant term (24) and add up to the linear coefficient (-11). These two numbers will be used to split the middle term and factor by grouping.

Step 1: Identify the Quadratic Expression

We start with the quadratic expression given by \[ a^2 - 11a + 24. \]

Step 2: Factor the Expression

To factor the expression, we need to find two numbers that multiply to $24$ (the constant term) and add up to $-11$ (the coefficient of the linear term). The numbers that satisfy these conditions are $-8$ and $-3$.

Step 3: Write the Factored Form

Using the identified numbers, we can express the quadratic in its factored form: \[ a^2 - 11a + 24 = (a - 8)(a - 3). \]