SOLUTION: simplify: 3x^3+18x^2-21x ___________ _

SOLUTION: simplify: 3x^3+18x^2-21x _________ x^3+5x^2-14x

Question 164241: simplify:
3x^3+18x^2-21x
______________
x^3+5x^2-14x
Answer by padmameesala(42) (Show Source): You can put this solution on YOUR website!
3x^3+18x^2-21x
=3x(x^2+6x-7) taking 3x as greatest common factor (g.c.f)
=3x(x^2+7x-x-7) the factors of -7 are 7 and -1 such that 7-1=6(coefficient of x)
=3x[x(x+7)-1(x+7)] taking x and -1 as g.cf.s from the 1st and last two terms
=3x(x+7)(x-1) taking x+7 as the g.c.f
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x^3+5x^2-14x
=x(x^2+5x-14)
=x(x^2+7x-2x-14) the factors of -14 are 7 and -2 which add up and give 5
=x[x(x+7)-2(x+7) taking x and -2 as g.cf.s from the 1st and last two terms
=x(x+7)(x-2) taking x+7 as the g.c.f

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SOLUTION: simplify: 3x^3+18x^2-21x ___________ __ x^3+5x^2-14x

SOLUTION: simplify: 3x^3+18x^2-21x _________ x^3+5x^2-14x