Factor 3x^2y^2 - 2xy^2 - 8y^2. Show your work.

3x^2y^2 - 2xy^2 - 8y^2 =

y^2 (3x^2 - 2x - 8) =

factoring with leading coefficient:

for ax2+bx+c find two numbers n, m, that m*n = a*c and m+n = b

3x^2 - 2x - 8

a=3, b=-2, c=-8

a*c = 3 * (-8) = - 24

-24 = (-6) * 4 and - 6+4=-2, so m=-6 and n=4

replace bx with mx + nx and factor by grouping

3x^2 - 2x - 8 = 3x^2 - 6x + 4x - 8 = 3x (x-2) + 4 (x-2) = (3x+4) (x-2)

answer:

3x^2y^2 - 2xy^2 - 8y^2 = y^2 (3x+4) (x-2)