Section 5.2 – Polynomials, Linear Factors, and Zeros
Solve by Factoring Review/Practice
x3  2 x 2  15 x  0
x3  x 2  12 x  0
With your table partner, answer the following questions.
What are the zeros of y  ( x  2)( x  1)( x  3) ? _________________
What is the degree?________ end behavior? _________ y-intercept? ___________
Sketch a graph of the polynomial.
Example:
( x  2) is a factor of f(x) iff f(2)=0
Similarly, if f(3)=0 then 3 is a zero and (x – 3) is a factor of f(x).
Writing a polynomial function from its zeros
Write a possible cubic function in standard form with zeros: 2, 2, and 3. _______________________
Write a possible quartic function in standard form with zeros: -2, -2, 2, and 3. _________________________
Exploration of the graphical behavior of x-intercepts (Multiplicity)
Relative Maximum or Minimum Values
Not all function have an absolute maximum or minimum value. If a graph has several turning points then the
function has relative maximum or minimum values.
What degree polynomial functions will NEVER have an absolute extreme point? Why?
Relative max or min values occur at an up-todown or down-to-up turning points.
Practice sketch polynomial functions.
f ( x)  x3  3x 2  24 x
g ( x)  3x3  x 2  5 x
Write a polynomial function from the graph.
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Example: The design of a digital box camera maximizes the volume while keeping the sum of the dimensions
at 6 inches. If the length must be 1.5 times the height, what would each dimension be?