The function is .
If is a rational zero, then is a factor of and is a factor of .
Here, and .
Write the possible value of in simplest form.
and .
Make a table and test some possible rational zeroes:
The depressed polynomial is .
The depressed polynomial is .
Observe the table:
Since , there is a zero at .
The depressed polynomial is .
The quadratic function is .
(Quadratic formula)
(Substitute and )
(Simplify)
(Add and simplify)
and (Separate two roots)
and (Simplify)
There is five real roots are , , , and .
The zeroes of the function are and .
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