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Vocabulary

Chapter 8 226

Adding and Subtracting Polynomials8-1

Tell whether each is an expression or an equation.

1. 3x 2 4 2. 14 5 8 1 6b 3. r6 4. 0 5 1

3x2

Write T for true or F for false.

5. Expressions with only numbers are always like terms.

6. An expression can have an equal sign.

7. Equations can be true, false, or open.

Vocabulary Builder

poly- (prefix) pahl ee

Related Words: many, several, polynomial, polygon

Definition: The prefix poly means “many” or “several” and is used to make compound words such as polygon.

Main Idea: Polynomials may contain one or several monomials.

Use Your Vocabulary

Complete each statement with a word from the list. Use each word only once.

polygon polygraph polynomial

8. A monomial or a sum of monomials is a 9.

9. A 9 test measures many tiny physical reactions of a person who is being questioned in order to determine whether that person is telling the truth.

10. A triangle is one example of a 9.

Review

polynomial

HSM11_A1MC_0801_T13363

3x2 + 3xy – y2

monomials

3x2, 3xy, –y2

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d.Problem 1

Problem 2

Polynomial DegreeName Using

DegreeNumberof Terms

Name UsingNumber of Terms

0

1

2

3

4

1

2

3

1

3

Constant

Linear

Quadratic

Cubic

Fourth degree

Monomial

Monomial

Trinomial

5x 9

6

4x2 7x 3

2x3

8x4 2x3 3x

Binomial

Trinomial

227 Lesson 8-1

Finding the Degree of a Monomial

Got It? What is the degree of the monomial 8xy?

11. Write the degree of each part of the monomial. Then find the degree of the monomial.

12. The degree of the monomial 8xy is .

Got It? What are the degrees of the monomials 27y4z and 11?

13. Write the degree of each part of each monomial. Then find the degree of the monomial.

27y4z 11

HSM11_A1MC_0801_T13365

8xy 8=

+degree ofeach part

degree of monomial+ =

• x y•

Adding and Subtracting Monomials

Got It? What is the sum 26x4 1 11x4? What is the difference 2x 2y4 2 7x 2y4?

14. Circle the like terms and underline the coefficients.

26x4 1 11x4 2x2y4 2 7x2y4

Simplify each expression.

15. 26x4 1 11x4 16. 2x2y4 2 7x2y4

5 Q 1 R x4 Use the Distributive Property. 5 Q 1 R x2y4

5 ? x4 Simplify within parentheses. 5 ? x2y4

You can name a polynomial based on its degree or the number of monomials it contains.

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Problem 3

Problem 4

Chapter 8 228

Classifying Polynomials

Got It? Write 2x 2 3 1 8x2 in standard form. What is the name of the polynomial based on its degree and number of terms?

17. Complete the model to write the polynomial in standard form.

18. In standard form, the polynomial 2x 2 31 8x2 is .

19. Circle the best name for the polynomial based on its degree.

constant linear quadratic cubic fourth degree

20. Circle the best name for the polynomial based on the number of terms.

monomial binomial trinomial

21. Now write the combined name for the polynomial.

____________________________________________________________________________________

Adding Polynomials

Got It? A nutritionist studies the U.S. consumption of carrots and celery and of broccoli over a 6-yr period. The nutritionist modeled the results, in millions of pounds, with the following polynomials.

Carrots and celery: 212x3 1 106x2 2 241x 1 4477

Broccoli: 14x2 2 14x 1 1545

In each polynomial, x 5 0 corresponds to the first year in the 6-yr period. What polynomial models the total number of pounds, in millions of carrots, celery, and broccoli consumed in the U. S. during the 6-yr period?

22. To add the polynomials, first group like terms. Then add or subtract the coefficients.

(212x3 1 106x2 2 241x 1 4477) 1 (14x2 2 14x 1 1545)

5 (212x3) 1 ( 1 14x 2) 1 ( 2 14x) 1 ( 1 1545)

5 1 2 1

23. The polynomial models the number of

pounds, in millions, consumed in the U. S. during the 6-yr period.

greatestdegree term

Write

Relatelesser

degree termleast

degree term

∙∙

+ +

HSM11_A1MC_0801_T13366

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d.Problem 5

Lesson Check

Now Iget it!

Need toreview

0 2 4 6 8 10

Math Success

229 Lesson 8-1

Subtracting Polynomials

Got It? What is a simpler form of (24m3 2 m 1 9) 2 (4m2 1 m 2 12)?

24. Subtract vertically.

24m3 1 m2 2 m 1 9 0 is the coefficient of each missing term.

2( m3

1 m2

1 m 2 ) Line up like terms.

24m3 1 m2 2 m 1 9

2 m3

2 m2

2 m 1 Rewrite the subtraction.

24m3 1 m2 2 m 1 Add each pair of terms.

25. Write the simplified form of (24m3 2 m 1 9) 2 (4m2 1 m 2 12).

• Do you UNDERSTAND?

Vocabulary Name the polynomial 5x2 1 2x 1 1 based on its degree and number of terms.

Underline the correct word(s) or number to complete each sentence.

26. The polynomial has two / three terms.

27. The greatest degree of a term is 0 / 1 / 2 .

28. Circle the best name for the polynomial.

cubic binomial cubic trinomial quadratic binomial quadratic trinomial

Check off the vocabulary words that you understand.

standard form classifying a polynomial cubic quadratic

Rate how well you can add and subtract polynomials.

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