Ch 6 (6-1 & 6-2) Portfolio Page
-- Algebra 2
Lesson 6-1: Polynomial Functions
--To classify polynomials –-To write polynomials in standard form
Degree – when the polynomial is in standard form, the degree is the highest power (exponent) on any
variable term
DEGREE
CLASSIFICATION
#
0
constant
1
monomial
1
linear
2
binomial
2
quadratic
3
trinomial
3
cubic
n
polynomial of n terms
4
quartic
5
quintic
OF TERMS
CLASSIFICATION
Examples: Write in standard form, then classify by degree and number of terms.
Graphs of Polynomial Functions
--General behaviors
A polynomial of degree n has at most ______ turns.
A polynomial of degree n has at most ______ x-intercepts.
If the leading coefficient of the polynomial is positive, the graph will _____________ to the right.
If the leading coefficient of the polynomial is negative, the graph will ____________ to the right.
If the degree of the polynomial is even, the graph will have the ____________ behaviors to the left & right
and have _____________ excepted zeros.
If the degree of the polynomial is odd, the graph will have _____________ behaviors to the left & right and
have ______________ excepted zeros.
A relative minimum or maximum of a function is the y-value of a point on the graph that is _____________/
_______________ than the nearby points on the graph.
CALCULATOR: 2nd Calc/Minimum(Maximum)/Left bound, Right bound, Guess. Y = 8x3 - 10x2 – x - 3
Lesson 6-2: Polynomials and Linear Factors
--To apply the Factor Theorem to polynomials
THE
FACTOR THEOREM
EXPRESSION (X – a) IS A LINEAR
FACTOR
OF A POLYNOMIAL IF AND ONLY IF THE VALUE
a
IS A ZERO OF THE RELATED POLYNOMIAL
FUNCTION
Ex1: If x – 3 is a factor of the
polynomial, then 3 is the zero.
Ex2: If 3 is a zero of the polynomial,
then x – 3 is a factor.
Examples: Find the zeros for each of the following and state the multiplicity of each.
Sketch.
1) (from factored form)
2) (from standard form)
y = x ( x – 3)( x + 4)2
y = - x3 + 3x2 + 10x
Examples: Given the following zeros, write the polynomial function in standard form:
3)
5)
4)
Y = 2x3 + 9x2 + 12x + 2
a)
6) Determine the intervals of increase
and decrease in interval notation.
What are the estimated
zeros? ____________
b) What is the estimate relative
maximum? ____________
c) What is the estimated relative
minimum? ______________
EQUIVALENT STATEMENTS
ABOUT
POLYNOMIALS
-4 is a solution/root of the equation x2 + 3x – 4 = 0
-4 is an x-intercept of the graph y = x2 + 3x – 4
-4 is a zero of the function y = x2 + 3x – 4
x + 4 is a factor of the expression x2 + 3x – 4.