SOLUTION: Find all the zeros of the polynomial function. f(x) = {{{ x^3-4x^2-11x+2}}}

Question 825385: Find all the zeros of the polynomial function.
f(x) =
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
As per the rational zero theorem,
the possible rational zeros of are integers factors of , meaning
-2, -1, 1, and 2.

We can try them all, starting by the easiest ones.
Trying 1 and -1 by substitution is easy enough:

.
That means that is not a zero of , and neither is .
If is a zero of , must be a factor of . If is a zero of , must be a factor of .
We could try -2 and 2 by substitution, but since in the end we will need to divide, we may choose just to try dividing by and by .
We would find that dividing by leaves a remainder,
but that divides evenly by , and
.
That means that is a zero of ,
and the remaining zeros are the zeros of .

We can use find the zeros of by solving the quadratic equation
either by using the quadratic formula or by "completing the square":

So either --> ,
or --> .

In sum, the zeros of are
, , and .
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