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Laney House
Mathematics
2 April, 18:07
Factor 3x^2y^2 - 2xy^2 - 8y^2. Show your work.
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Roman Sanford
2 April, 18:09
0
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)
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