Advanced Algebra
Unit 2: Polynomial Functions
Excerpts from Georgia
Department of Education
Webinar September 5, 2013
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October 2013
Warm-Up
Trina has a conjecture: “Pick any two integers, Look at the sum of their squares, the difference of
their squares, and twice the product of the two integers you chose. Those three numbers are the
sides of a right triangle.”
Is the conjecture true, if so prove it, if not modify it to be true and show it is true.
Solution:
Let m and n be our positive integers.
Show
Show
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October 2013
Therefore:
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October 2013
What’s the main idea of Unit 2?
• Use complex numbers in polynomial identities and equations.
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.
• Perform arithmetic operations on polynomials.
• Understand the relationship between zeros and factors of polynomials.
• Use polynomial identities to solve problems.
• Solve systems of equations.
• Represent and solve equations and inequalities graphically.
• Analyze functions using different representation
Concepts & Skills to Maintain from Previous Grades
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Combining like terms and simplifying expressions
Long division
The distributive property
The zero property
Properties of exponents
Simplifying radicals with positive and negative radicands
Factoring quadratic expressions
Solving quadratic equations by factoring, taking square roots, using the quadratic formula
and utilizing graphing calculator technology to finding zeros/ x-intercepts
Observing symmetry, end-behaviors, and turning points (relative maxima and relative
minima) on graphs
Writing explicit and recursive formulas for geometric sequences
Websites to help with the above:
http://www.crctlessons.com/
www.aplusmath.com
www.aaamath.com
melissa.stewart@hallco.org
October 2013
ENDURING UNDERSTANDINGS
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Viewing an expression as a result of operations on simpler expressions can sometimes
clarify its underlying structure.
Factoring and other forms of writing polynomials should be explored.
The Fundamental Theorem of Algebra is not limited to what can be seen graphically; it
applies to real and complex roots.
Real and complex roots of higher degree polynomials can be found using the Factor
Theorem, Remainder Theorem, Rational Root Theorem, and Fundamental Theorem of
Algebra, incorporating complex and radical conjugates.
A system of equations is not limited to linear equations; we can find the intersection
between a line and a polynomial
Asking when two functions have the same value for the same input leads to an equation;
graphing the two functions allows for finding approximate solutions to the equation.
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October 2013
Example:
Suppose
is a polynomial of degree
If r is a real number such that
Dividing
where
Substituting
by
show that
is evenly divisible by
gives:
is a polynomial of degree
and
is a real number.
we find:
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October 2013
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The student edition for Unit 2 can be found at
https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx On the left
side, please look under mathematics, Accelerated Geometry B/Advanced Algebra.
Then, the right side has a pull-down menu to access the units.
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Additional parent guides will be posted to the parent resource page on
http://www.hallco.org/boe/index.php (right hand menu) as they become available.
melissa.stewart@hallco.org
October 2013