SOLUTION: Factor the polynomial as a product of linear factors, find the zeros of the polynomial and state the multiplicity of the zeros. P(x)= x^3-3x^2-9x+27

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the polynomial as a product of linear factors, find the zeros of the polynomial and state the multiplicity of the zeros. P(x)= x^3-3x^2-9x+27      Log On


   

Question 692482: Factor the polynomial as a product of linear factors, find the zeros of the polynomial and state the multiplicity of the zeros.
P(x)= x^3-3x^2-9x+27
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29=+x%5E3-3x%5E2-9x%2B27
I would factor by grouping:
P%28x%29=+%28x%5E3-3x%5E2%29%2B%28-9x%2B27%29
Taking out a common factor for each group/bracket:
P%28x%29=+x%5E2%28x-3%29%2B%28-9%29%28x-3%29
Taking out %28x-3%29 as a common factor:
P%28x%29=+%28x%5E2-9%29%28x-3%29
And since x%5E2-9=%28x%2B3%29%28x-3%29,
highlight%28P%28x%29=+%28x%2B3%29%28x-3%29%28x-3%29%29 or highlight%28P%28x%29=+%28x%2B3%29%28x-3%29%5E2%29

So the zeros are highlight%28x=-3%29 with multiplicity highlight%281%29,
and highlight%28x=3%29 with multiplicity highlight%282%29