SOLUTION: factorise completely the following a) x^9-y^9 B)x^4-5x^3+5x^2+5x-6

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Question 1116335: factorise completely the following
a) x^9-y^9
B)x^4-5x^3+5x^2+5x-6

Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A) You can use the"special product %28A-B%29%28A%5E2%2BAB%2BB%5E2%29=A%5E3-B%5E3 twice,
with system%28A=x%5E3%2CB=y%5E3%29 the first time, and system%28A=x%2CB=y%29 the second time.

The last expression is completely factorized.
A polynomial of the form A%5E2%2BAB%2BB%5E2 is positive as long as AB%3C%3E0 ,
so it cannot be factored.

B) x%5E4-5x%5E3%2B5x%5E2%2B5x-6
takes the value 0 for x=1 and for x=-1 ,
so %28x-1%29 and %28x%2B1%29 are factors.
Dividing by both, you find
x%5E4-5x%5E3%2B5x%5E2%2B5x-6=highlight%28%28x-1%29%28x%2B1%29%28x%5E2-5x%2B1%29%29
The last expression is completely factorized,
unless you wanted to include %28x-%285%2Bsqrt%2821%29%29%2F2%29 and %28x-%285-sqrt%2821%29%29%2F2%29 as factors,
because the zeros of x%5E2-5x%2B1 are the irrational numbers %285+%2B-+sqrt%2821%29%29%2F2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
factorise completely the following
a) x^9-y^9
B)x^4-5x^3+5x^2+5x-6
Correct answers: