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# 6.11: Finding Rational and Real Zeros

Difficulty Level: At Grade Created by: CK-12
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Practice Finding Zeros of Polynomials

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Estimated24 minsto complete
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Estimated24 minsto complete
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### Vocabulary Language: English

factor theorem

The factor theorem states that if $f(x)$ is a polynomial of degree $n>0$ and $f(c)=0$, then $x-c$ is a factor of the polynomial $f(x)$.

Rational Root Theorem

The rational root theorem states that for a polynomial, $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$, where $a_n, a_{n-1}, \cdots a_0$ are integers, the rational roots can be determined from the factors of $a_n$ and $a_0$. More specifically, if $p$ is a factor of $a_0$ and $q$ is a factor of $a_n$, then all the rational factors will have the form $\pm \frac{p}{q}$.

Remainder Theorem

The remainder theorem states that if $f(k) = r$, then $r$ is the remainder when dividing $f(x)$ by $(x - k)$.

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