Algebra 2

I am trying to factor a 4th degree polynomial that does not have any rational roots. I need to somehow get it factored into two quadratics. Anyone know of a method to use.

3x^4 - 8x^3 - 5x^2 + 16x - 5

Two of the irrational roots are 1.135.. and 0.382.. but that won't help you with the factoring.

You might try factoring the fourth order polynomial into two quadratics of the form
(3x^2 + ax + b)(x^2 + cx + d)
and picking a, b, c and d to get the coefficents in the fourth order polynomial to agree. For example,
bd = -5
3c + a = -8
ad + bc = 16
3d + b + ac = -5

Where did you get that form of factoring? I have never seen any books that address factoring a fourth degree polynomial like the one I presented.

Thank you very much.

I got it from your suggestion that it be factored into quadratics. I got the two real roots by essentially graphical means. There is a specific formula for the roots of fourth order polynomials, but it is very long and complicated. I think they are hoping you will find it by trial and error.

I could understand getting the roots by graphical means if the book had put the answers in decimal form. However, they had the answers in exact form and I knew the only way to get them would be by solving a quadratic equation. Thanks once again for your help.

  1. 👍 0
  2. 👎 0
  3. 👁 169
asked by Brenda

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra 2

    I am trying to factor a 4th degree polynomial that does not have any rational roots. I need to somehow get it factored into two quadratics. Anyway know of a method to use. 3x^4 - 8x^3 - 5x^2 + 16x - 5

    asked by Brenda on March 8, 2007
  2. algebra 2

    Factor completely with respect to the integers. 1. 9x^2 - 4 2. x^3 + 64 3. 200x^2 - 50 4. 8x^3 - 64 5. x^3 + x^2 + x + 1 6. x^3 - 2x^2 + 4x - 8 7. 2x^3 + 4x^2 + 4x + 8 8. 2x^3 + 3x^2 -32x - 48 9. 7x^3 + 14x^2 + 7x 10. 6x^3 - 18x^2

    asked by anonymous on January 9, 2007
  3. Algebra

    Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find

    asked by Marissa on August 10, 2007
  4. algebra

    Factor this polynomial: F(x)=x^3-x^2-4x+4 Try to find the rational roots. If p/q is a root (p and q having no factors in common), then p must divide 4 and q must divide 1 (the coefficient of x^3). The rational roots can thuis be

    asked by bailey on January 19, 2007
  5. Math

    Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots

    asked by Jass on February 27, 2017
  6. Alegbra 2

    Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

    asked by Chelsey on January 26, 2018
  7. Algebra 2

    1) Find the roots of the polynomial equation. x^3-2x^2+10x+136=0 2) Use the rational root theorem to list all problem rational roots of the polynomial equation. x^3+x^2-7x-4=0. Do not find the actual roots.

    asked by Anonymous on December 4, 2017
  8. Math

    How to factor x^3 - 3x^2 + 4 =0 Use D'Alembert's Rational Roots Theorem. Any rational roots of the form of p/q (p and q assumed to be relatively prime) must be such that p divides the constant term (in this case 4) and q divides

    asked by Ed on July 14, 2007
  9. Algebra 2

    Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1

    asked by Ryan on March 13, 2015
  10. algebra

    using the rational root theorem to list all possible rational roots of the polynomial equation x^3-x^2-x-3=0 possible answers -3,-1,1,3 1,3 -33 no roots

    asked by jayson on November 12, 2012

More Similar Questions