SOLUTION: Let f(x)= x cube-8x squared+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1.

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Question 92468This question is from textbook Algebra and Trigonometry
: Let f(x)= x cube-8x squared+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1. This question is from textbook Algebra and Trigonometry

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+x%5E3+-+8x%5E2+%2B+17x+-+9
~
f%28x%29+-+f%281%29+=+0
x%5E3+-+8x%5E2+%2B+17x+-+9+-+%281+-+8+%2B+17+-+9%29+=+0
x%5E3+-+8x%5E2+%2B+17x+-+9+-+1+=+0
x%5E3+-+8x%5E2+%2B+17x+-+10+=+0
x%5E3+-+8x%5E2+%2B+17x+-+10+=+0
~Use Synthetic Division, Descartes Rule of Signs, +- p/q, or whatever you know
%28x+-+1%29%28x+-+2%29%28x+-+5%29+=+0
x = 1, 2, 5
graph%28300%2C300%2C-1%2C6%2C-6%2C1%2Cx%5E3+-+8x%5E2+%2B+17x+-+10%29