Algebra 2

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. factoring

    can this equation be factored further? y= x^4+2x^3+4x^2+8x+16 Not in the real number system. If you plot the function, you will see the minimum is at x=-1.1 (approx) and y is positive. At no x does the function equal zero, so there
  2. math

    first question: could x^5-1 simplified? what is the limit of cuberoot(x^2-5x-4) as x approaches 4?
  3. 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 …
  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 +/1, …
  5. 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
  6. Algebra2

    Find the polynomials roots to each of the following problems: #1) x^2+3x+1 #2) x^2+4x+3=0 #3) -2x^2+4x-5 #3 is not an equation. Dod you omit "= 0" at the end?
  7. 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 all …
  8. College Algebra

    I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational …
  9. College Algebra--Still Confused

    I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational …
  10. 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.

More Similar Questions