Find the complete factorization of P(x) = x^4-2x^3+5x^2-8x+4?  the roots i found so far are : (x+2)(x-1)(x+4)  when you multipy it out, it is x^3+5x^2+2x-8. What is the last root is what i'm trying...

Find the complete factorization of P(x) = x^4-2x^3+5x^2-8x+4? 

the roots i found so far are :

(x+2)(x-1)(x+4)  when you multipy it out, it is x^3+5x^2+2x-8. What is the last root is what i'm trying to figure out. 

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lfryerda eNotes educator | Certified Educator

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If you have already found a factor of a polynomial, you can use synthetic division to find a polynomial that has smaller degree and shares the remaining factors of the polynomial.  In this case, let's use the factor x-1.

Then synthetic division gives:

1 | 1  -2  5  -8  4

 ...

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