Question 773231
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Factor
X^4-x^3-27x+27
X^3+2x^2-3x-6
Ans:
{{{x^4-x^3-27*x+27}}}
=
{{{x^3*(x - 1) -27*(x - 1)}}}
{{{(x^3 - 27)*(x - 1)}}}
{{{(x^3 - 3^3)*(x - 1)}}}
{{{(x - 3)*(x^2 + 3*x + 9)*(x - 1)}}} ---> since a^3 - b^3 = (a - b)*(a^2 + ab + b^2)


2)
{{{x^3+2*x^2-3*x-6}}}
=
{{{x^2*(x + 2) - 3*(x + 2)}}}
=
{{{(x^2 - 3)*(x + 2)}}} which can be further simplified as
{{{(x + sqrt(3))*(x - sqrt(3))*(x + 2)}}}
:)
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