math

posted by .

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 -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. college algebra

    use rational zeros theorem to find all the real zeros in the polynomial function. use zeros to factor f over real numbers. f(x)=x^3+10x^2-13x-22 find real zeros of f?
  2. 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)=x^3-8x^2-31x-22
  3. calculus

    use 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)=x^3-8x^2-31x-22 **please show work**
  4. math

    usethe rational zero theorem to find all real zeros of the polynomisl function.Use the zeros to factor f over the real numbers. f(x)=x^4+2x^33-7x^2-8x+12 what are the real zeros?
  5. math

    use the rational zero theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers: f(x)=4x^4+9x^3+30x^2+63x+14 I cant even find sample problems to help me figure this out. help me …
  6. 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
  7. rational zeros theorem

    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)=25x^4+26x^3+126x^2+130x+5 Find the real zeros x= Use the real zeros to factor f f(x)=
  8. pre calculus

    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)=x^4+2x^3-7x^2-8x+12 I am totally lost, please help?
  9. 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)=9x^4+28x^3+66x^2+196x+21 Find the real zeros of f Use the real zeros to factor f f(x)=
  10. 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)= x^4+6x^3-11x^2-24x+28 Molon

More Similar Questions