 # Find the rational zeros and then other zeros of the polynomial function f(x) = x^{3} - 17x^{2} + 55x + 25, that is, solve f(x) = 0 Factor f(x) into linear factors Dolly Robinson 2020-10-27 Answered
Find the rational zeros and then other zeros of the polynomial function
that is, solve $f\left(x\right)=0$
Factor $f\left(x\right)$ into linear factors
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To find the rational zero and other zeros of the polynomial

Factor $f\left(x\right)$ into linear factors
Let us solve the equation.
$f\left(x\right)=0$

$\because$ the constant term has factors 1 and 5.
Let us whether these can be zeros.

can not be zero of f(x).

is a rational zero of f(x).
We can write,

Now we only need to solve the quadratic equation.

Then

Therefore, there is only one rational zero, 5 and other zeros are

The factorization of f(x),

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