SOLUTION: factor the polynomial and use the factored form to find the zeros( enter answers as a comma-separated list.) P(x)=x^3+3x^2-9x-27 x=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial and use the factored form to find the zeros( enter answers as a comma-separated list.) P(x)=x^3+3x^2-9x-27 x=      Log On


   

Question 977234: factor the polynomial and use the factored form to find the zeros( enter answers as a comma-separated list.)
P(x)=x^3+3x^2-9x-27
x=
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Try synthetic division to test for the possible roots, plus or minus 1,3,9. The quadratic result of the first found root can then be finished using general solution for a quadratic equation.

Testing -3,
Find quotient, x%5E2-9.

That tells you because of further obvious factorability of the resulting quotient,
%28x%2B3%29%28x%2B3%29%28x-3%29=P%28x%29
Roots are -3 and +3. The -3 root is of multiplicity two.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E3%2B3x%5E2-9x-27
f%28x%29=%28x%5E3%2B3x%5E2%29-%289x%2B27%29
f%28x%29=x%5E2%28x%2B3%29-9%28x%2B3%29
f%28x%29=%28x%5E2-9%29%28x%2B3%29
f%28x%29=%28x%5E2-3%5E2%29%28x%2B3%29
f%28x%29=%28x-3%29%28x%2B3%29%28x%2B3%29
set f%28x%29=0
0=%28x-3%29%28x%2B3%29%28x%2B3%29
if 0=%28x-3%29=>x=3
if0=%28x%2B3%29=>x=-3 multiplicity 2
so, zeros are:(x%5B1%5D,x%5B2%5D,x%5B3%5D)=(3,-3,-3)