Algebra by Adding and Subtracting Polynomials

This Time, With Polynomials

Adding and Subtracting Multiplying Polynomials (OPT 4 Day 14)

TOPIC 2
Solving Quadratic Equations

This Time,
With Polynomials

Solutions, More
or Less

Transforming Solutions

The Missing Link

1

2

3

4

5

Ladies and Gentlemen,
Please Welcome the
Quadratic Formula!

IMPORTANT INFORMATION

• If you do not complete the Quizizz or Delta Math assignments, you

will not be excused from any Mathia assignment.

• If you started OPT 3 and/or OPT 4 with me and you do not finish,

you will be required to complete all of the Mathia assignments

• Emails will be sent to parents this week advising them of your

current progress in my class.

Learning Goals

•Name polynomials by number of terms or degree.

•Understand that you can perform operations on functions as well as
numbers.

•Add and subtract polynomials.

•Explain why polynomials are closed under addition and subtraction.

monomial

binomial

trinomial

closed, closure

KEY TERMS

OPT 4: Day 19B: MATHIA Assignment:

Practice Set 07 IS EXCUSED ONLY IF YOU
PARTICIPATE IN TODAY’S LESSON. You
must show POSITIVE participation in chat

AND Quizizz

Activity 1

Categorizing Polynomials

Previously, you worked with linear expressions in the form ax + b and quadratic
expressions in the form ax2 + bx + c. Each is also part of a larger group of expressions
known as polynomials.

Recall that a polynomial is a mathematical expression involving the sum of powers in one
or more variables multiplied by coefficients. A polynomial in one variable is the sum of
terms of the form axk, where a is any real number and k is a non-negative integer.

In general, a polynomial is of the form a1xk + a2xk−1 + ... + anxo. Within a polynomial, each
product is a term, and the number being multiplied by a power is a coefficient.

Multiple Choice

Rewrite by combining like terms: $$-3x+4y-9x-5y$$

• There are no like terms

• -6x + y

• -12x - y

• -12x + y

Multiple Select

In the following expressions, which terms are "like terms?"

2xy²+ 5x²y - 7xy + xy²​ ​

​ ​ ​ ​ ​

• xy
• x^2y
• xy^2

• 2xy^2

Polynomial

General form

a₁x^k + a₂x^k−1 + ... + a_nx^o

• each product is a term
• the number being multiplied by a power is a coefficient.

1.

Write each term from the worked
example and identify the coefficient,
power, and exponent. The first term
has already been completed for you.

Activity 1

WORKED EXAMPLE

The polynomial m3 + 8m2 − 10m + 5 has four terms. Each term is written in the form axk.
• The first term is m3 .
• The power is m3, and its coefficient is 1.
• In this term, the variable is m and the exponent is 3.

2.

Identify the terms and coefficients in each polynomial.

a) − 2x2 + 100x

b) 4m3 − 2m2 − 5 c) y⁵ − y + 3

You name polynomials according to the number of terms they have.

•Polynomials with only one term are monomials.

•Polynomials with exactly two terms are binomials.

•Polynomials with exactly three terms are trinomials.

The degree of a term in a polynomial is the exponent of the term.

•The greatest exponent in a polynomial determines the degree of the polynomial.

Linear functions are polynomials with a degree of 1 because you can write them in the form ax + b.

Activity 1

Is it a Polynomial?

Yes IF,

• the exponent is POSITIVE
• the exponent is an INTEGER
• the exponent IS NOT A VARIABLE

3.

Khalil says that 3x−2 + 4x − 1 is a trinomial with a degree of 1 because 1 is the greatest
exponent. Jazmin disagrees and says that this is not a polynomial at all because the power
on the first term is not a whole number. Who is correct? Explain your reasoning.

4.

Determine whether each expression is a polynomial. Explain your reasoning.

Activity 1

A polynomial is in general form when the terms are in descending order, starting with the term with the greatest degree and ending with the term with the least degree.

5.

Revisit the cards you sorted in the Getting Started.

a)

Identify any polynomial not written in general form and rewrite it in general form on
the card.

b)

Identify the degree of each polynomial and write the degree on the card.

Activity 1

1.

Write Each polynomial in general form.

2.

Classify the polynomial by its number of terms

3.

Classify the polynomial by degree

4.

Identify all the coefficients

Classifying Polynomials

You can perform operations on functions.
Adding and Subtracting Polynomial Functions

Add or subtract to rewrite each expression.

Categorize

Options (12)

$$\frac{4}{5}r^3+\ \frac{2}{5}r-1$$  

$$-13s\ +\ 6$$  

$$25-18m^2$$  

$$125p$$  

$$-\frac{2}{3}$$  

$$12.5t^3$$  

$$-6$$  

$$-6x^2+4x$$  

$$78j^3-3j$$  

$$4-7h$$  

$$y^2-4y+10$$  

$$-3+7n+n^2$$  

Classify each polynomial by number of terms.

Monomial

Binomial

Trinomial

You can perform operations on functions.
Adding and Subtracting Polynomial Functions

Add or subtract to rewrite each expression.

Combining Functions and Addressing Closure

In this activity, you will practice adding and subtracting polynomials.
1.

Analyze each student’s work. Determine the error and make the necessary corrections.

Activity 4

Activity 4

> Consider each polynomial function.

2.

Determine each function. Write your answers in general form. Is the function a polynomial?

A(x) = x3 + 5x2 − 9 B(x) = −3x2 − x + 1 C(x) = 2x2 + 7x D(x) = −2x2 − 8x

a) J(x) = A(x) + C(x)

b)

K(x) = D(x) − B(x)

c) L(x) = C(x) + D(x)

Activity 4

> Consider each polynomial function.

2.

Determine each function. Write your answers in general form. Is the function a polynomial?

A(x) = x3 + 5x2 − 9 B(x) = −3x2 − x + 1 C(x) = 2x2 + 7x D(x) = −2x2 − 8x

d)

M(x) = B(x) − A(x)

e)

N(x) = A(x) − C(x) − D(x)

Given:

Find:

Activity 4

3.

Are the functions J(x), K(x), L(x), M(x) and N(x) polynomial functions? Explain why or
why not.

When an operation is performed on any of the numbers in a set and the result is a number
that is also in the same set, the set is closed, or has closure, under that operation.

For example, the set of integers is closed under addition and subtraction. That means
whenever you add or subtract two integers, the result is also an integer.

WHEN YOU ADD OR SUBTRACT

POLYNOMIALS, THE RESULT IS ALWAYS A

POLYNOMIAL. THEREFORE,

POLYNOMIALS ARE CLOSED UNDER

ADDITION AND SUBTRACTION.

Word Cloud

In one or two words, share how comfortable you feel about adding and subtracting polynomials.