Posted by **Chama** on Wednesday, March 27, 2013 at 8:15am.

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.

f(x)=2x^3-x^2+2x-1

- College Algebra -
**Reiny**, Wednesday, March 27, 2013 at 9:35am
Possible rational zeros:

± 1, ± 1/2

f(1) = 2 - 1 + 2 - 1 ≠0

f(-1) = -2 - 1 - 2 - 1 ≠0

f(1/2) = 1/4 - 1/4 + 1-1 = 0 , yeahh, (2x - 1) is a factor

Using long division...

2x^3-x^2+2x-1 = (2x - 1)(x^2 + 1)

so x = 1/2 or x^2 = -1

x = 1/2 or x = ± i

so the only real zero is x=1/2

- College Algebra -
**Chama**, Wednesday, March 27, 2013 at 9:58am
How do you use the real zeros to factor f?

- College Algebra -
**Steve**, Wednesday, March 27, 2013 at 10:29am
if x=a is a real zero. (x-a) is a factor. Divide f(x) by (x-a) and see what the quotient is. Maybe you can factor it, maybe not. In this case, not.

- College Algebra -
**Chama**, Wednesday, March 27, 2013 at 10:33am
Ok thank you

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