Find the real zeros of f. Use the real zeros to factor f.
The real zeros of the function are .
And it is factored as .
The given function is of degree three, so it has at most three real zeros.
Now all the coefficients are integers so we use the rational zeros theorem.
The factors of the constant term are
The factors of the leading coefficient are
So the possible rational zeros are
The graph of the function is given as
The graph has two turning points, so it will have three real zeros.
From the graph, it appears that is a zero of the function. On performing synthetic division we get
As the remainder is zero so is a zero of the function.
And the quotient is the depressed polynomial. So the given function is factored as
Equating the depressing polynomial with zero and factoring by grouping we get
So the other zeros are
All the three real zeros of the function are .
And it can be written in factored form as .
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