SOLUTION: Use the rational root theorem and the factor theorem to help solve the equation. A polynomial equation of degree n has n solutions, and any solution of multiplicity p is counte

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the rational root theorem and the factor theorem to help solve the equation. A polynomial equation of degree n has n solutions, and any solution of multiplicity p is counte      Log On


   

Question 1023686: Use the rational root theorem and the factor theorem to help solve the equation.
A polynomial equation of degree n has n solutions, and any solution of multiplicity p is counted p times.
x^3 − 5x^2 − 13x − 7 = 0

Please help me solve. Thank you
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+-5x%5E2+-13x+-7+=+0....write -5x%5E2 as 2x%5E2-7x%5E2 and -13x as -14x%2Bx
x%5E3%2B2x%5E2-7x%5E2-14x%2Bx-7+=+0....group
%28x%5E3-7x%5E2%29%2B%282x%5E2-14x%29%2B%28x-7%29+=+0
x%5E2%28x-7%29%2B2x%28x-7%29%2B%28x-7%29+=+0
%28x-7%29%28x%5E2%2B2x%2B1%29+=+0
%28x-7%29%28x%2B1%29%5E2+=+0
solutions:
if %28x-7%29=+0->x=7
if %28x%2B1%29%5E2+=+0->x=-1...multiplicity 2

+graph%28+600%2C+600%2C+-10%2C+10%2C+-30%2C+10%2C+x%5E3+-5x%5E2+-13x+-7+%29+