College Algebra

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

asked by Chama
  1. 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

    posted by Reiny
  2. How do you use the real zeros to factor f?

    posted by Chama
  3. 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.

    posted by Steve
  4. Ok thank you

    posted by Chama

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