Question

factor the trinomial.
$a^2 + 6a - 16$

select the correct choice below and, if necessary, fill in the answer b
a. $a^2 + 6a - 16 = \square$ (factor completely.)
b. the trinomial is not factorable.

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-16\) and add up to \(6\). Let's list the factor pairs of \(-16\): \((-1, 16)\), \((1, -16)\), \((-2, 8)\), \((2, -8)\), \((-4, 4)\). Checking the sums: \(-1 + 16 = 15\), \(1 + (-16) = -15\), \(-2 + 8 = 6\), \(2 + (-8) = -6\), \(-4 + 4 = 0\). So the numbers are \(-2\) and \(8\).

Step2: Factor the trinomial

Using the numbers from Step 1, we can factor \(a^2 + 6a - 16\) as \((a - 2)(a + 8)\) because \(a^2 + 6a - 16 = a^2 - 2a + 8a - 16 = a(a - 2) + 8(a - 2) = (a - 2)(a + 8)\).

Answer:

A. \(a^{2}+6a - 16=(a - 2)(a + 8)\)