SOLUTION: please help me solve this 2x^8-10x^7+10x^6

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Question 356290: please help me solve this
2x^8-10x^7+10x^6
Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
please help me solve this
2x^8-10x^7+10x^6

this is not an equation, it is a trinomial, a polynomial with 3 terms, if it were an equation it would be set to zero, and you would attempt to determine if there is a solution for x

however can see if this can be factored
2x^8 - 10x^7 + 10x^6
2x^6(x^2 - 5x + 5)

the x^2 - 5x + 5 can not easily be factored

would need to use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
and plug in 1 for a, -5 for b, and 5 for c
this would result in x1 = (1/2)(5 + sqrt(5)) and x2 = (1/2)(5 - sqrt(5))

testing these factors results in:
2x^6(x - (1/2)(5 + sqrt(5)))(x - (1/2)(5 - sqrt(5)))
2x^6(x^2 - (1/2)x(5 - sqrt(5)) - (1/2)x(5 + sqrt(5)) + (1/2)(1/2)(5 + sqrt(5)(5 - sqrt(5)))
2x^6(x^2 - (5/2)x + (1/2)xsqrt(5) - (5/2)x - (1/2)xsqrt(5) + (1/4)(25 - 5))
2x^6(x^2 - 5x + (1/4)(20))
2x^6(x^2 - 5x + 5)