Question

Factor d^2 - 12d + 32 (d - 4) (d + 8) right?

Answer 1

d^2 - 12d + 32
(d - 4) (d + 8) right?

Answer 2

- in both brackets

Answer 3

Could you explain how?

Answer 4

FOIL method

Answer 5

it should be both negative because the sum of them must be equal to -12

Answer 6

\[d^2-12d+32\]\[(d+a)(d+b) = d(d+b) + a(d+b) = d^2 + bd + ad + ab\]\[\qquad=d^2+ (a+b)d + ab\]

Let's compare:
\[d^2-12d+32\]\[d^2+(a+b)d + ab\]
Those will be equal if we choose \(a,b\) such that \(a+b=-12\) and \(ab = 32\)

So, we need a pair of factors of \(32\) that sum to \(-12\). \(-8,-4\) is such a pair:\[-8*-4 = 32\]\[-8-4 = -12\]

Our factoring is therefore\[(d-4)(d-8) = d^2-8d-4d+32 = d^2-12d+32\]