Combining Polynomials

​Adding/Subtracting Polynomials

by Sam R

Welcome to Algebra 1

Live Session 21:
I’m glad you are here!
Please make sure your desk/workspace is ready and read through the announcements.

Intro Question/Review of Last Session:
Simplify the following expression:

At Desk/Workspace:

● Pencil (preferred) or pen

● Paper

● Calculator

Agenda:

● Review

● Polynomials

● Adding/Subtracting

● Exit Ticket

Upcoming Assignments:
Studies: 6.1.1 Quizzes: 6.1.3
Checkup: 6.1.2
Practice: 6.1.4

●

Steps

o

Step 1: Identify any like terms (shown in
matching colors)

o

Step 2: Combine like terms by
adding/subtracting the coefficients

o

Step 3: Write the final simplified answer

Intro Question

Multiple Choice

Are the following terms 'like' or 'unlike'....

3a

-7a

• Like

• Unlike

Multiple Choice

Are the following terms 'like' or 'unlike'....

-5b

-12b

• Like

• Unlike

Multiple Choice

Simplify W-10+9W-3

• 10W+7

• 9W-5

• 9W +13

• 10W -13

Multiple Choice

Simplify -V-10V

• -11V

• -9V

• 9V

• 11V

●

What is a polynomial?

o

The term polynomial refers to any
mathematical expression that has one or
more terms.

▪

Polynomials cannot have variables in the
denominator of a fraction.

▪

Any exponents in a polynomial must be
whole numbers.

Polynomials

Polynomials

Multiple Choice

What is the lead coefficient?

• 150

• −20

• −9.8

• 2

Multiple Choice

What is the constant term?

• 3

• 2

• −5

• 0

Multiple Choice

What is the constant term?

• 18

• −8

• 4

• 3

Multiple Choice

What is the leading coefficient?

• 2

• 1

• −25

• 0

Multiple Choice

What is the degree of this trinomial?

• 1

• 2

• −20

• 0

Multiple Choice

What is the degree of this polynomial?

• 1

• 2

• 3

• −1

Multiple Choice

How many terms are in a monomial?

• 1

• 2

• 3

• 4+

Multiple Choice

How many terms are in a trinomial?

• 1

• 2

• 3

• 4+

Multiple Choice

How many terms are in a binomial?

• 1

• 2

• 3

• 4+

Multiple Choice

What type of polynomial is this?

• monomial

• binomial

• trinomial

• polynomial

Multiple Choice

What type of polynomial is this?

• monomial

• binomial

• trinomial

• polynomial

●

Just like when we solve linear equations,
we can simplify polynomial expressions
by combining like terms!

o

Remember; for something to be a like term,
it needs both the same variables and the
same exponents.

●

Looking at this example, what terms
could I combine?

○

Combine x^2 and 2x^2 because they both
have x^2

○

Combine x and 2x because they both have x

○

Combine the constants (1 & 1) because
they both do not have a variable

Adding & Subtracting Polynomials

Multiple Choice

Add the polynomial (-3x + 4) + (8x - 5)

• 5x - 9

• 5x - 1

• 11x - 1

• 11x - 9

• None of these

Multiple Choice

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

Tips for Success

-Fill out the study guide 6.1.1

-Complete the checkup 6.1.2

-Complete the practices 6.1.4

-Complete Quiz 6.1.5

Exit Ticket

Solve this:

Wrap-Up

If you have any questions or concerns about this course, please say behind so we can

chat!

Multiple Choice

Add the polynomials.
(2x + 5y) + (3x - 2y)

• 3x + 5y

• 5x + 3y

• 5x + 7y

• 7xy + 1xy

Open Ended

Simplify the following:

-3x+4

+ (-2x^2 +6x - 1)

​If you finish the Polynomials Lesson early...

​If you complete your Polynomials Lesson early, work on the following tasks....

​

​1. Take the 6.1 Quiz over parts of polynomials/adding and subtracting them.

​

2. Work through any missing assignments or past due assignments.

​

​3. Begin the 6.2 Study.