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

## Answer This Question

## Related Questions

- College algebra - Use the rational zeros theorem to find all the real zeros of ...
- college algebra - use rational zeros theorem to find all the real zeros in the ...
- rational zeros theorem - Use the rational zeros theorem to find all the real ...
- college algebra - use the rational zeros theorem to find all the real zeros of ...
- college algebra - 1. solve the following logarithmic equation log_8(x+8)+log_8(x...
- college algebra - use the rational zeros theorem to find all the real zeros of ...
- pre calculus - use the rational zeros theorem to find all the real zeros of the ...
- calculus - use rational zeros theorem to find all the real zeros of the ...
- math - usethe rational zero theorem to find all real zeros of the polynomisl ...
- calculus - use the rational zeros theorem to find all the real zeros of the ...

More Related Questions