Operations with Polynomials Lesson Seed
Perform arithmetic operations on polynomials.
A.APR.A.1 Understand that polynomials for a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Interpret the structure of expressions.
A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
MP3:
MP5:
MP6:
MP7:
MP8:
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Common Core Algebra II, Unit 4
Teacher’s Notes:
Since this is a cross-cutting standard from Common Core Algebra I, assess student prior understanding
and review as needed. This lesson seed provides potential activities to practice adding, subtracting, and
multiplying polynomial expressions.
Warm-Up:
Have students choose a partner, or assign partners. Have students watch the Youtube video on
polynomial operations. (http://www.youtube.com/watch?v=uSxrUSPW5u8) (Note: This is mainly a
review for students that might not remember how to add, subtract, or multiply polynomials from Algebra
I. The students should feel free to watch all of the video or watch only the parts of the video they might
need. The video should be available to the students throughout the activity for the students to refer to as
needed.)
Lesson Task/Activity:
Polynomial Operations: Tic-Tac-Toe
1. Keep students with their partners. Explain the directions of the Tic-Tac-Toe activity.
(Teacher/Student Resource: Tic-Tac-Toe Game Play Directions) Distribute game boards to the
students. (Game boards increase in difficulty as students continue to progress through the
activity.) (Teacher/Student Resource: Tic-Tac-Toe Game Boards)
2. Have students begin playing Tic-Tac-Toe. (Look for evidence of MP 3, 5, 6, 7, 8)
3. Have students submit the completed game boards at the end of the activity.
Closure:
As an exit ticket, have students write a note to the students in next year’s Algebra II class summarizing
how to add, subtract, and multiply polynomial expressions.
Level 1
(x 5  x 3  x)
(8x 2  x 3  1)
(2x 4  5x 3  10x)
(x 4  2x 3  x  4)

3x x 2  2

(x 2  5x  5)
(12x  8)
(2x  1)(x  4)
(x 3  2x 2  1)
(3x 5  x 3  2x  1)
(2x 4  x 3  4 x 2  x)
(2x 5  x 4  4 x 3  2)
(x  1)(x  3)
(x 3  2x 2  5x  9)
(10x 4  12x 2  1)
Level 2
(18x  2)(4  2x)
(x 2  3x 3  11x  4)
(21x  x 2  3x 3 )
(3x 4  4x 2  13)
(12x 4  23x 5  12x 3  2)
(3x  4w  z)
(8x  11w  8z)
14x 2 (7x 4  13)
(27x 8  4x 6  11x 5  14x)
(x  2)(x 2  2x  1)
(x  3)(x 2  5x  6)
Level 3
(17x 2  12x 5  18x 6  7)
x  13x 6  9 
(12x  7)2
x
2
 3x  2 x 2  2x  1

2x  33
x
2
 x  2 x2  x  2
4x  1x 3  x 2  x  2 
x
2
 7x  18 x 2  10x  20




x  23
3x  8 2
 x  3
4