Divide 12 into two parts such that their product is 32.
Let the first number be ‘X’, so the other number will be ’(12–X)’.
∵ X (12 – X) = 32
12X – X2 = 32
X2 – 12X + 32 = 0
On factorising further,
X2 – 4X – 8X + 32 = 0
X(X – 4) – 8(X – 4) = 0
(X – 4)(X – 8) = 0
So, X = 4 or 8
∴ The numbers are 4 and 8.