Transcript web intro polynomials

P OLYNOMIALS
P OLYNOMIAL D EFINITIONS
 Greatest
(GCF)
Common Factor
 Composite Number
 Prime Number
 Prime Polynomial
 Foil Method
 Factored Form
 Factoring
 Quadratic Expression
 Quadratic
Equation
 Quadratic Formula
 Inverse Variation
 Product Rule
 Rational Function
 Rational Equation
 Extraneous Solutions
P OLYNOMIALS

What are polynomial and rational expressions
and how can they be simplified?

What are the characteristics of the graphs of
rational functions?

What are the techniques for solving rational
equations?

How can polynomial or rational expressions be
connected to real world applications?
P OLYNOMIAL AND R ATIONAL E XPRESSIONS
R ATIONAL E QUATIONS & F UNCTIONS
CLE 3102.3.2; SPI
3102.3.2; CFU
3102.3.7;
CFU3102.3.2; SPI
8.1 Monomials and Factoring
3102.3.3;
CFU3102.3.8;
CLE 3102.3.8; SPI
3102.3.3; SPI
8.3 Quadratic Equations x2 + bx
3102.3.10; CFU
+c=0
3102.3.3; CFU
3102.3.9
CLE
3102.3.8;
SPI
8.4 Quadratic Equations ax2 +
3102.3.3; SPI
bx + c = 0
3102.3.10
CLE 3102.3.8; SPI
8.5 Quadratic Equations 3102.3.10; SPI
Difference of Squares
3102.3.3
7.6 Multiplying a Polynomial
by a Mononmial
11.1 Inverse Variation
11.2 Rational Functions
11.3 Simplifying Rational
Expressions
11.4 Multiplying and Dividing
Rational Expressions
11.5 Dividing Polynomials
11.6 Adding and Subtracting
Rational Expressions
11.8 Rational Equations
Understand and apply properties in order to perform operations with, evaluate, simplify, and factor
expressions and polynomials.; Operate with polynomials and simplify results.; Use various models (including
area models) to represent products of polynomials.
Find the GCF of the terms in a polynomial.; Understand and apply properties in order to perform operations
with, evaluate, simplify, and factor expressions and polynomials.; Factor polynomials.
Solve and understand solutions of quadratic equations with real roots.; Factor polynomials.; Find the solution
of a quadratic equation and/or zeros of a quadratic function.; Justify correct results of algebraic procedures
using extension of properties of real numbers to algebraic expressions.; Find two binomial factors of a
quadratic expression.
Solve and understand solutions of quadratic equations with real roots.; Factor polynomials.; Find the solution
of a quadratic equation and/or zeros of a quadratic function.
Solve and understand solutions of quadratic equations with real roots.; Find the solution of a quadratic
equation and/or zeros of a quadratic function.; Factor polynomials.
Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation,
CFU3102.3.19;
quadratic, and square root function. Use technology where appropriate.; Use technologies appropriately to
CLE 3102.1.7; SPI
develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate
3102.1.2
and reliable models.; Write an equation symbolically to express a contextual problem.
Understand and use relations and functions in various representations to solve contextual problems.; Operate
CLE 3102.3.6; SPI
with, evaluate, and simplify rational expressions including determining restrictions on the domain of the
3102.3.4; SPI
variables.; Determine domain and range of a relation, determine whether a relation is a function and/or
3102.3.7
evaluate a function at a specified rational value.
CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Operate with, evaluate, and
3102.3.4; SPI simplify rational expressions including determining restrictions on the domain of the variables.; Apply
3102.1.3
properties to evaluate expressions, simplify expressions, and justify solutions to problems.
CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Operate with, evaluate, and
3102.3.4;
simplify rational expressions including determining restrictions on the domain of the variables.
CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Find the solution of a quadratic
3102.3.10
equation and/or zeros of a quadratic function.
CFU3102.3.10; Add, subtract, multiply, and divide rational expressions and simplify results.; Understand and apply
CLE 3102.3.3; SPI operations with rational expressions and equations.; Operate with, evaluate, and simplify rational
3102.3.4
expressions including determining restrictions on the domain of the variables.
CLE 3102.3.3; SPI Understand and apply operations with rational expressions and equations.; Determine domain and range of a
3102.3.7
relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.
7.6 M ULTIPLY A P OLYNOMIAL BY A
M ONOMIAL
CLE 3102.3.2 Understand and apply properties in order to
perform operations with, evaluate, simplify, and factor
expressions and polynomials.
SPI 3102.3.2 Operate with polynomials and simplify results.
CFU 3102.3.7 Use various models (including area models) to
represent products of polynomials.
D ISTRIBUTIVE P ROPERTY
M ODELING WITH A LGEBRA T ILES
2 X ( X + 3)
X
=2 X 2 + 6 X
1
1
1
X
X2
X
X
X
X
X2
X
X
X
M ODELING WITH A LGEBRA T ILES
3 X ( X - 2)
X
=3 X 2 – 6 X
1
1
X
X2
X
X
X
X2
X
X
X
X2
X
X
M ODELING WITH A LGEBRA T ILES
2 X ( X - 4)
X
=2 X 2 – 8 X
1
1
1
1
X
X2
X
X
X
X
X
X2
X
X
X
X
M ULTIPLY M ONOMIAL VS
P OLYNOMIAL
Use Distributive
Property
-2x2(3x2 -7x + 10)
-2x2(3x2) = -6x4
-2x2(-7x) = +14x3
-2x2(+ 10) = -20x2
= -6x4 +14x3 -20x2
S IMPLIFY
THE
Use Distributive
Property
3(2t2-4t-15) + 6t(5t + 2)
Combine Like
Terms
6t2-12t-45 + 30t2 + 12t
36t2 +0t -45
36t2 - 45
E QUATION
P RACTICE A SSIGNMENT

Page 442, 18 – 30 even
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DO ALL EVEN

LATE ASSIGNMENTS WILL
NEED TO DO PAGE 831 1-6
ADDITIONAL