a^2+6a-16

Answer 1

To factor the expression \(a^2 + 6a - 16\), we need to find two numbers that multiply to -16 and add up to 6.

The factors of -16 are:
1, -16
-1, 16
2, -8
-2, 8
4, -4
-4, 4

Among these pairs, the pair that adds up to 6 is 2 and -8.

So, we can rewrite the expression:

\(a^2 + 6a - 16 = a^2 + 2a - 8a - 16\)

\(= a(a + 2) - 8(a + 2)\)

\(= (a - 8)(a + 2)\)

Therefore, \(a^2 + 6a - 16\) factors to \((a - 8)(a + 2)\).