Unformatted text preview: f (x). Since f has degree n, there can be at most n of
these factors. The next section provides us some tools which not only help us determine where the
real zeros are to be found, but which real numbers they may be.
We close this section with a summary of several concepts previously presented. You should take
the time to look back through the text to see where each concept was ﬁrst introduced and where
each connection to the other concepts was made. 204 Polynomial Functions
Connections Between Zeros, Factors and Graphs of Polynomial Functions
Suppose p is a polynomial function of degree n ≥ 1. The following statements are equivalent:
• The real number c is a zero of p
• p(c) = 0
• x = c is a solution to the polynomial equation p(x) = 0
• (x − c) is a factor of p(x)
• The point (c, 0) is an x-intercept of the graph of y = p(x) 3.2 The Factor Theorem and The Remainder Theorem 3.2.1 205 Exercises 1. (An Intermediate Algebra review exercise) Use polynomial long division to perform t...
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