SOLUTION: Determine the x-intercepts of {{{f(x)=(x^2-6x)^2-2(x^2-6x)-35}}}

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Question 224747: Determine the x-intercepts of f%28x%29=%28x%5E2-6x%29%5E2-2%28x%5E2-6x%29-35
Answer by LtAurora(115) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%28x%5E2-6x%29%5E2-2%28x%5E2-6x%29-35
Substitute out the messy bit:
u=%28x%5E2-6x%29
This gives a more reasonable looking equation:
f%28x%29=u%5E2-2u-35
Which can be factored as:
f%28x%29=%28u%2B5%29%28u-7%29
Then, substitute x back in:
f%28x%29=%28%28x%5E2-6x%29%2B5%29%28%28x%5E2-6x%29-7%29
This yields
f%28x%29=%28x%5E2-6x%2B5%29%28x%5E2-6x-7%29
Which can factor down to:
f%28x%29=%28x-6%29%28x-1%29%28x-7%29%28x%2B1%29
Thus the x-intercepts are:
x=6,1,7,-1
This type problem could also be done with synthetic division, but this particular one factors without too much difficulty.