Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. Find the real zeros of f(x) = 5x^{3} - x^{2} + 5x - 1

Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of
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Given: find all real zeros of and use the zeros to factor f over the real numbers.
Used concept :
Rational zeros theorem:
Let P(x) is a polynomial. if p/q isazetoof P(x) then p is the factor of the constant term of P(x) and q is the factor of the leading coefficient of P(x).
Let $\frac{p}{q}$ is the rational zero of the given polynomial.
Here, p is a factor of the constant term $-1$
and q is a factor of the leading coefficient 5.
So, the possible value of
and
Now, the possible value of
Now, check the value of function

So, the zero of the given function is $\frac{1}{5}$ in real numbers.

Jeffrey Jordon