SOLUTION: Factor X^4-x^3-27x+27 X^3+2x^2-3x-6

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Question 773231: Factor
X^4-x^3-27x+27
X^3+2x^2-3x-6
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Factor
X^4-x^3-27x+27
X^3+2x^2-3x-6
Ans:
x%5E4-x%5E3-27%2Ax%2B27
=
x%5E3%2A%28x+-+1%29+-27%2A%28x+-+1%29
%28x%5E3+-+27%29%2A%28x+-+1%29
%28x%5E3+-+3%5E3%29%2A%28x+-+1%29
%28x+-+3%29%2A%28x%5E2+%2B+3%2Ax+%2B+9%29%2A%28x+-+1%29 ---> since a^3 - b^3 = (a - b)*(a^2 + ab + b^2)


2)
x%5E3%2B2%2Ax%5E2-3%2Ax-6
=
x%5E2%2A%28x+%2B+2%29+-+3%2A%28x+%2B+2%29
=
%28x%5E2+-+3%29%2A%28x+%2B+2%29 which can be further simplified as
%28x+%2B+sqrt%283%29%29%2A%28x+-+sqrt%283%29%29%2A%28x+%2B+2%29
:)