Use the rationals theorem
posted by Karlee .
Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=2x^3x^2+2x1

follow the same steps I just showed you in your last post
http://www.jiskha.com/display.cgi?id=1364332046 
I like this variant which makes use of candidates that turn out not to be a zero. This works as follows.
The possible zeroes are:
x = 1,1,1/2,1/2 (1)
We have:
f(1) = 2
If we put
g(t) = f(1+t)
then the coefficient of t^3 is 2 and the constant term is f(1) = 2, the possible zeroes are thus:
t = +/1 , +/2, +/ 1/2
The possible zeroes of f are thus:
x = 1+t = 0,2,1,3,1/2,3/2
But since all the possible zeroes are listed in (1), we can strike out the elements that are not on that list. We are thus left with:
x = 1,1/2
Then since 1 is not a zero, the only possible rational zero is 1/2, which is indeed a zero. Then you can proceed by dividing f(x) by x1/2 and find the zeroes of the quadratic.
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