SOLUTION: Find the complete factorization of p(x)= x^4-2x^3+10x^2-18x+9

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Question 1099745: Find the complete factorization of p(x)= x^4-2x^3+10x^2-18x+9

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What will you learn if I do that?
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Try the factors of 9 first.
--> 1, 3 & 9, plus and minus.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the complete factorization of p(x)= x^4-2x^3+10x^2-18x+9
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  x%5E4+-+2x%5E3+%2B+10x%5E2+-+18x+%2B+9 = 

= %28x%5E4+-+2x%5E3+%2B+x%5E2%29 + %289x%5E2+-+18x+%2B+9%29 = 

= x%5E2%2A%28x%5E2+-+2x+%2B+1%29 + 9%2A%28x%5E2-2x%2B1%29 = 

= x%5E2%2A%28x-1%29%5E2 + 9%2A%28x-1%29%5E2 = 

= %28x%5E2%2B9%29%2A%28x-1%29%5E2.

Grouping and re-grouping method.