Question 1032313: Use the rational root theorem and the factor theorem to help solve the equation. Be sure that the number of solutions for the equation agrees with the property below, taking into account multiplicity of solutions.
A polynomial equation of degree n has n solutions, and any solution of multiplicity p is counted p times.
x^3 − x^2 − 21x + 45 = 0
Please help me solve this, thank you!!
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
The rational root theorem says that the rational roots of this equation are among the divisors of the constant term, which is 45 in this case.
So, check these numbers: +/-1, +/-3, +/-5, +/-9, +/-15, +/-45.
When you find the root x = n, divide the original polynomial by (x-n)
(long division).
You will get the polynomial of the degree 2 instead of 3.
Then you will be able to complete your analysis.
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