SOLUTION: Find all roots of the polynomial x cube-x squared+16x-16.

Question 92878This question is from textbook Algebra and Trigonometry
: Find all roots of the polynomial x cube-x squared+16x-16. This question is from textbook Algebra and Trigonometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all roots of the polynomial x cube-x squared+16x-16.
x^3-x^2+16x-16
Since the coefficients add up to zero x=1 is a root and x-1 is a factor.
Use synthetic division to find the other factors and roots.
------------------------
1)....1....-1....16....-16
.......1.....0.....16..|..0
Remainder is zero because 1 is a root.
Quotient is x^2+16
-------------------
Factoring x^2+16 you get (x+4i)(x-4i)
-----------------------
All the roots are: x=1, x= 4i, x= -4i
==================
Cheers,
Stan H.
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