Question

factor completely
a² + 10a + 24
(a + 4)(a + 6)
4(a + 6)(a + 9)
6(a + 7)(a + 8)
not factorable

Explanation:

Step1: Recall factoring trinomials

To factor \(a^2 + 10a + 24\), we need two numbers that multiply to \(24\) and add up to \(10\).

Step2: Find the two numbers

The factors of \(24\) are: \(1\) and \(24\) (sum \(25\)), \(2\) and \(12\) (sum \(14\)), \(3\) and \(8\) (sum \(11\)), \(4\) and \(6\) (sum \(10\)). So the numbers are \(4\) and \(6\).

Step3: Write the factored form

Using the numbers \(4\) and \(6\), we can factor the trinomial as \((a + 4)(a + 6)\) since \((a + 4)(a + 6)=a^2+6a + 4a+24=a^2 + 10a + 24\).

Answer:

A. \((a + 4)(a + 6)\)