SOLUTION: Find all the real zeros of the function. h(x)= {{{x^4-4x^3-9x^2+16x+20}}}

Question 825381: Find all the real zeros of the function.
h(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
-20, -5, -4, -2, -1, 1, 2, 4, 5, and 20.

We can try them all, starting by the easiest ones.
Trying 1 and -1, we find is one zero:

Since is a zero of , must be a factor of .
That means that divides evenly by , with no remainder.
Dividing by we get
, so
.
(The division can be done by "synthetic division", or whatever method you have been taught in class).

As per the rational zero theorem,
the possible rational zeros of are integers factors of , meaning
-20, -5, -4, -2, -1, 1, 2, 4, 5, and 20.
We know that because otherwise
We can find that either by substituting 2 for x,
or by dividing by .
,
and dividing we find that
.

So,
.

Quadratic polynomial is easy to factor as
, so
.

and for
, , , and .
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