SOLUTION: Factoring : a)x^4+(x-4)^4-82 b)(x^2-a)^2-6x^2+4x+2a Help me ! Thanks

Question 1120666: Factoring :
a)x^4+(x-4)^4-82
b)(x^2-a)^2-6x^2+4x+2a
Help me ! Thanks
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
One approach is to set the first to equal 0
x^4+(x-4)^4-82=0
x=3 can be see to be a solution
x=1 can also be seen to be a solution
This product of factors (x-3) and (x-1), or x^2-4x+3, can be divided into the expanded polynomial 2x^4-16x^3+96x^2-256x+174
or its equivalent of x^4-8x^3+48x^2-128x+87
to yield the quadratic x^2-4x+29, which is prime and the third factor of the original polyomial.

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