Math 30 College Algebra February 16, 2000

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Math 30 --- College AlgebraFebruary 16, 2000

• Section 2.1 and 2.2 due
• Section 2.3 questions
• Section 2.4
• Break
• Section 2.5
• Assignment 13 and 14

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AnnouncementsFebruary 16, 2000

• Exam 2 Two weeks from today
• No Class Monday

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Quiz (due)
Given Show
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Division
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Polynomial Division
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Remainder Theorem
If a number c is substituted for x in the
polynomial f(x), then the result f(c) is the
remainder that would be obtained by dividing f(x)
by x-c. That is, if then
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Factor Theorem
For a polynomial f(x), if f(c)0, then x-c is a
factor of f(x). That is, if you know a zero, you
know a factor and if you know a factor, you know
a root.
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Fundamental Theorem of Algebra
Every polynomial of degree n, ngt0, with complex
coefficients, has at least one zero in the system
of complex numbers.
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Fundamental Theorem of Algebra
Corollary Every polynomial of degree n, ngt0, with
complex coefficients, can be factored into n
linear factors (not necessarily unique).
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Complex Zeros
If a complex number , is a zero of a
polynomial functions f(x) with real coefficients,
then its conjugate, , is also a zero. Nonreal
zeros occur in conjugate pairs.
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Rational Zeros Theorem
Let where all the coefficients are integers.
Consider a rational number denoted by p/q, where
p and q are relatively prime (having no common
factor besides -1 and 1). If p/q is a zero of
P(x), then p is a factor of and q is a factor of
.
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Intermediate Value Theorem
For any polynomial function P(x) with real
coefficients, suppose that for , P(a) and P(b)
are of opposite signs. Then the function has a
real zero between a and b.
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Assignments 13 and 14

• For Wednesday Read 2.6 and 2.7
• Section 2.2 and2.3 homework is due Wednesday.
• Homework 2.4 pbs 5, 11, 15, 17, 19, 25, 27, 31,
  35, 41, 43-46, 49, 51
• Homework 2.5 pbs 1, 3, 9, 11, 15, 17, 23, 25,
  31, 37, 39, 43, 51, 57-60