SOLUTION: Ok, so I was told to 'factor the trinomial completly' with this problem... x^7-x^6-64x+64 ..... I think I am sapose to combine like terms so it would be in the form x^2+bx+c

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ok, so I was told to 'factor the trinomial completly' with this problem... x^7-x^6-64x+64 ..... I think I am sapose to combine like terms so it would be in the form x^2+bx+c       Log On


   

Question 203973: Ok, so I was told to 'factor the trinomial completly' with this problem...
x^7-x^6-64x+64 .....
I think I am sapose to combine like terms so it would be in the form x^2+bx+c where x is one.
So I combined them and got x-64x+64 and I know I have to factor but I am not sure if I can....because the product is a*c=64 and the sum is -64 and I am not sure what two numbers multiply together that equal 64 that also add together to equal -64.
help?

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
To factor, use "grouping" technique:
x^7-x^6-64x+64
= (x^7-x^6)-(64x-64)
= x^6(x-1)-64(x-1)
= (x^6-64)(x-1)
But wait, we still factor left term:
= (x^3-8)(x^3+8)(x-1)