algebra

posted by bailey

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, +/2 and +/4. If you insert these values you find that the roots are at

x = 1, x = 2 and x = -2. This means that

x^3-x^2-4x+4 = A(x - 1)(x - 2)(x + 2)

A = 1, as you can see from equation the coefficient of x^3 on both sides.


Typo:

The rational roots can be
+/-1, +/-2 and +/-4

Respond to this Question

First Name

Your Answer

Similar Questions

  1. math

    Factor: x^3 - 3/4x - 1/4 The answer is: (x - 1)(x + 1/2)^2 How do I learn to do that?
  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 …
  3. math

    Still looking at how to solve these... Both are cubic polynomials?
  4. algebra 1 [fractions]

    8y^4+10y^3+12y+15 ----------------- 4y+5 divide then express your anwser as a polynomial or mixed expression Do i look for its common factors then start dividing?
  5. math

    Still having problems solving this... 2x(2x + 1)^2 = 312 I started with: 2x(2x+1)(2x+1)-312 = 0 2x(4x^2+4x+1)-312 = 0 8x^3+8x^2+2x -312 = 0 Now what?
  6. 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 the …
  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. 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 <--?
  9. 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.
  10. algebra 2

    Suppose the polynomial f(x) has the following roots: 1+6sqrt2, 2−sqrt6, and 6+sqrt2. If f(x) has only rational coefficients, the Irrational Root Theorem indicates that f(x) has at least three more roots. What are the three additional …

More Similar Questions