lesson 8: adding and subtracting polynomials · 2016-09-01 · hart interactive – algebra 1 m1...

Hart Interactive – Algebra 1

M1 Lesson 8 ALGEBRA I

Lesson 8: Adding and Subtracting Polynomials

Exploratory Exercise Kim was working on a problem in math when she ran across this problem.

Kim’s dad said, “I remember doing something like this in school.” He then drew two arcs on her paper.

1. Talk to your partner about what Kim’s dad was trying to show. Then complete Kim’s problem.

In Lesson 7, you mainly used the commutative and associative properties, and only looked at examples of the

distributive property. In this lesson we’ll look closer at the distributive property and then in the next lesson

you’ll extend your knowledge about this important property.

2. What does the word “distribute” mean? Give two examples of the word in everyday use.

3. In math, distribute means to multiply out the parts of an expression. How does this definition relate to

your definition from Exercise 2?

Distribute and simplify if possible.

2(3x + 5)

Distribute and simplify if possible.

2(3x + 5)


S.67

This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org

This file derived from ALG I-M1-TE-1.3.0-07.2015

This work is licensed under a

Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Distribute in real-life means to hand out. For example: He distributed the blankets to all the campers. I distributed the food samples at the store.

Equally. Multiply to each/every term.



4. In each example below, one or more mistakes were made when distributing. Circle the mistakes and then

write the correct expression.

A. 2(3 5)6 5x

x+ =+

B. 2

3

(2 3)2 3x xx

− =

−

C. 3(3 4)9 4xx

− + =− +

D. 4(4 5)16 20xx

− − =− −

E. 2

2

2(4 6)8 12x

x− + =

− +

F. 3

4 2

(4 5 6)4 5 6x x xx x x

− − + =

− +

5. What was the common mistake made in 4A, 4B and 4C?

6. What was the common mistake made in 4D, 4E and 4F?


S.68





The term outside of the parenthesis was not distributed to the second term in the parenthesis.

Mistakes with the negative sign. 4D and 4E were not multiplied to the second term. 4F was not multiplied to any term.



ADDING POLYNOMIALS

7. Add the following polynomials by combining like terms. Be careful – you will have to distribute in a few of

them.

A. (3 5) (7 3)x x+ + − B. 2(2 3) (7 2)x x− + + C. (3 4) ( 4 7)x x+ + − −

D. (4 5) 2(3 1)x x− + + E. 2 22(4 6) (7 9 3)x x x− + + − + F. 3 2(4 5 6) (6 7 3)x x x x x− − + + + −

SUBTRACTING POLYNOMIALS

When subtracting polynomials, you will need to distribute the negative sign to all the terms in the

parentheses.

8. Subtract these polynomials and then combine like terms.

A. 2 2(8 9) (6 2)x x− − − B. (5 2) (3 9)x x− − + C. 5( 1) 6( 1)x x+ − −

D. 6 5 (5 6)x x− − − E. 2 230 20 2(10 5 7)x x x− − − + F. 3 27 (8 9 4)x x x x− + −


S.69







9. Determine which word matches each definition.

Word Bank

Polynomial Monomial Binomial Trinomial

Degree of a Term Degree of a Polynomial Standard Form of a

Polynomial

Definition Word

A. The sum of the exponents of the variable symbols that appear in the monomial

B. A polynomial with only two terms

C. The sum (or difference) of monomials

D. The degree of the monomial term with the highest degree

E. The terms are rewritten so that the terms are in order from greatest degree to least degree

F. An algebraic expression generated using only the multiplication operator (×). Thus, it does not contain + or − operators.

G. A polynomial with only three terms

10. Go back to Exercises 7 and 8 and write each polynomial in standard form, if it isn’t already in standard

form, and then determine the degree of the resulting polynomial.

11. Janie writes a polynomial expression using only one variable, 𝑥𝑥, with degree 3. Max writes a polynomial

expression using only one variable, 𝑥𝑥, with degree 7.

A. What can you determine about the degree of the sum of Janie’s and Max’s polynomials?

B. What can you determine about the degree of the difference of Janie’s and Max’s polynomials?


S.70





Degree of a termBinomial

Trinomial

Degree of polynomialStandard form of a polynomialMonomial

Polynomial

It must have a degree of 7.

It must have a degree of 7.

lesson 8: adding and subtracting polynomials · 2016-09-01 · hart interactive – algebra 1 m1...

Documents