Question 825059: Let P(x)= 2x^3-5x^2-4x+3
Find the complete factorization of P.
I think this needs to be a Polynomial but I'm not sure where to begin. I understand how to do everything else with the equation. This one kind of screws me up. Please help.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! We are looking for factors which are the 0's of 2x^3-5x^2-4x+3
I start by looking for rational roots and of course, 1 or -1 is worth checking first
if x = 1, we get 2 -5 -4 +3 = -4 so 1 is not a 0
if x = -1, we get -2 -5 +4 +3 = 0 so -1 is a 0 and x+1 is a factor. Now use synthetic division
-1 | 2 -5 -4 3 |
| -2 7 -3 | |
| 2 -7 3 0 |
This leaves us with the smaller polynomial 2x^2 -7x +3 and we can factor this smaller polynomial into (2x-1) * (x-3), therefore the complete factorization of
2x^3-5x^2-4x+3 is (x+1)*(2x-1)*(x-3)
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