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

Question 825414: Find all the zeros of the polynomial function.
f(x) =
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The possible rational zeros are +1/1 and +2/1 (which simplify to +1 and +2). Trying these we find that only -2 is actually a zero:

-2  |   1   -4   -11   2
-----       -2    12  -2
       ------------------
        1   -6     1   0

The zero in the lower right corner is the remainder. (It is also f(-2)!) Since it is zero then what we divided by (x-(-2)) [or (x+2)] divides evenly. So (x+2) is a factor of f(x). Not only that but the rest of the bottom row tells us what the other factor is. The "1 -6 1" translates into . So now

The other zeros of f(x) will come from the second factor. Since it is a quadratic that won't factor, we can use the quadratic formula:

Simplifying...

which is short for or

So the three zeros for f(x) are: -2, and
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