Exponents and Exponential Functions

Lesson 2

Objective

Add and subtract polynomial expressions using properties of operations.

Common Core Standards

Core Standards

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  • A.APR.A.1 — 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.

Foundational Standards

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  • 7.EE.A.1

  • 8.EE.C.7

Criteria for Success

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  1. Understand a polynomial as a sum of terms in which each term includes only multiplication as an operator. 
  2. Identify the degree and leading coefficient for polynomials. 
  3. Find the sum or difference of polynomials using the properties of operations and write polynomials in standard form.

Tips for Teachers

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In Lessons 2 and 3, students briefly study polynomials in order to apply properties of operations and exponents to mathematical situations. They will study polynomials more in depth in Algebra 2.

Anchor Problems

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Problem 1

A polynomial is given below.

$${10-4x+x^5+3x^2-x-6x^2}$$

a.   Write the polynomial using the fewest number of terms possible. Write the polynomial in standard form. 

b.   Identify the degree and leading coefficient of the polynomial. 

Guiding Questions

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Problem 2

Find each sum or difference. Write your answers in standard form.

a.   $${(4x^2+x+7)+(2x^2+3x+1)}$$

b.   $${(3x^3-x^2+8)-(x^3+5x^2+4x-7)}$$

c.   $${3(x^3+8x)-2(x^3+12)}$$

d.   $${(3+1)+6(p-8)-(p+2)}$$

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 8Exercise 4

Algebra I > Module 1 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Problem 1

Simplify the expression. Write your answer in standard form.

$${x^2-4(x-8x^2)+(5+10x)}$$

Problem 2

Write a polynomial addition problem that has a sum of $${m^8-m^6+m^4}$$.