Today in Pre-Calculus

1
Today in Pre-Calculus

• Go over homework
• Need a calculator
• Review Chapter 2

2
Rational Zeros Theorem

• tells us how to make a list of potential rational
  zeros for a polynomial function with integer
  coefficients.
• If p be all the integer factors of the constant
  and q be all the integer factors of the leading
  coefficient in the polynomial function then,
• gives us a list of potential rational zeros

3
Finding zeros

• Find all the zeros of f(x) x4 2x3 x2 4x
  6 and identify the zeros as real or nonreal and
  rational or irrational. Show the use of the
  rational zeros theorem and all work.

4
Degree of Polynomial

• If the polynomial is in standard form, find the
  highest power, this is the degree of the
  polynomial.
• example f(x) 5x3 4x5 7x2 8x 12
• If the polynomial is in factored form, add up the
  exponents for each of the factors.
• example f(x) (x 7)(x 2)3(x 5)2

5
Multiplicity of a Zero

• If f is a polynomial function and (x c)m is a
  factor of f, then c is a zero of multiplicity m.
  (c is a repeated zero).
• Example f(x) (x 2)3(x1)2
• If the multiplicity is odd, then the graph
  crosses the x-axis at (c,0) and the value of f
  changes sign at x c
• If the multiplicity is even, then the graph
  touches (but does not cross) the x-axis at (c,0)
  and the value of f does NOT change sign at x c

6
Sketch the graph

• f(x) (x 2)3(x1)2

7
Solving Inequalities

• Without graphing find the intervals where
• f(x) 0 or UND
• f(x)gt0
• f(x)lt0

8
Homework

• Pg 209 39-42all
• Pg 225 49, 51, 53, 54
• Pg 264 25, 26, 45,46