# College Algebra

posted by Chama

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

1. Reiny

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

2. Chama

How do you use the real zeros to factor f?

3. Steve

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.

4. Chama

Ok thank you

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