A2.A-APR.1
2011
Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Perform arithmetic operations on polynomials
Standards: Understand that polynomials form a system analogous to the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Essential Questions
How do we perform binary
operations on polynomials?
When performing binary
operations on polynomials,
will it ever not be closed?
Content Statements
Understand the definition
of a polynomial.
Understand the concepts of
combining like terms and
closure.
Add, subtract, and multiply
polynomials and understand
how closure applies under
these operations.
Assessments
I.
Evaluate:
35 · 3-1
Enduring Understandings
Understanding the concept of
closure.
Activities, Investigation, and Student Experiences
Student reflection (writing assignment)
 Similarities between addition, subtraction, and
multiplication on numbers and on polynomials
Student Investigation
 Show that division is not closed
Activity: Finding a Pattern
x2 – 1 = (x – 1)(x – 1)
x3 – 1 = (x – 1)(x2 + x + 1)
4
x – 1 = (x – 1)(x3 + x2 + x + 1)
x5 – 1 = ?
n
In general, how can x – 1 be factored? Show that this
factorization works by multiplying the factors.
A2.A-APR.1
  2  2 
  
 3  


2011
2
II. Simplify:
a b 
2
5 3
y 7 x3
y 4 x 0
x
x
3
3
III.
 
 5 x  7 x  5

 x 2  6  2x 2  4x  8
On July 21, 2004, the national debt of the U.S.
was $7,282,000,000,000. The population at that
time was 294,000,000. Suppose the national debt
was divided evenly among everyone in the U.S.,
how much would each person owe?
Equipment Needed:
Internet access
Teacher Resources:
http://www.khanacademy.org/video/adding-polynomials-withmultiple-variables?playlist=Developmental+Math+2
Larson 2012