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Posted by on Friday, January 4, 2013 at 7:52am.

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

f(x)=x^4+2x^3-7x^2-8x+12

x=

f(x)=

  • math - , Friday, January 4, 2013 at 8:48am

    try factors of 12
    on the first try, I got f(1) = 0
    so x-1 is a factor

    by long algebraic or by synthetic division , I got
    x^4+2x^3-7x^2-8x+12
    = (x-1)(x^3 + 3x^2 - 4x - 12)

    grouping the x^3 + 3x^2 - 4x - 12
    = x^2(x+3) - 4(x+3)
    = (x+3)(x^2-4)
    = (x+3)(x+2)(x-2)

    so
    x^4+2x^3-7x^2-8x+12
    = (x-1)(x-2)(x+2)(x+3)

    (had I been patient, I would have found
    f(2) = 0, f(-3)=0 and f(-2) = 0 as well)

    the zeros are
    1, 2, -2, -3

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