<PRE><B>Question 164241</B>
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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