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6.11: Finding Rational and Real Zeros

Difficulty Level: At Grade Created by: CK-12
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Vocabulary

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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Date Created:
Mar 12, 2013
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