## Algebra: A Combined Approach (4th Edition)

$-2a^{2}$ + 10a +12 First, take out -2 common: $-2a^{2}$ + 10a +12 = -2($a^{2}$ - 5a - 6) ....(since (-2)(-5) = 10 and (-2)(-6) = 12) Now we need two numbers such that their sum is -5 and their product is -6. Thus the two numbers are -6 and 1. Check the two numbers are right: Sum = -6 + 1 = -5 Product = (-6)(1) = (-6). Thus, $a^{2}$ - 5a - 6 = $a^{2}$ - 6a + a - 6 = a(a -6) + 1(a - 6) =(a + 1)(a - 6).