8-1
Adding and Subtracting
Polynomials
Vocabulary
Review
Tell whether each is an expression or an equation.
1. 3x 2 4
2. 14 5 8 1 6b
4. 0 5 13x2
3. 6r 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
3x2 + 3xy – y2
Related Words: many, several, polynomial, polygon
monomials
Definition: The prefix poly means “many” or “several” and is used
to make compound words such as polygon.
3x2, 3xy, –y2
Main Idea: Polynomials may contain one or several monomials.
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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.
Chapter 8
226 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
polynomial
poly- (prefix) pahl ee
Problem 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.
8xy = 8
degree of
each part
•
x
+
12. The degree of the monomial 8xy is •
y
+
=
degree of monomial
.
Got It? What are the degrees of the
monomials 27y4z and 11?
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13. Write the degree of each part of each monomial. Then find the degree of the monomial.
27y4z
11
Problem 2 Adding and Subtracting Monomials
Got It? What is the sum 26x4 1 11x4? What is the difference 2x 2y4 2 7x 2y4?
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
14. Circle the like terms and underline the coefficients.
26x4 1 11x4 2x2y4 2 7x2y4
Simplify each expression.
15. 26x4 1 11x4 5 Q 5 16. 2x2y4 2 7x2y4
1 R x4 ? x4 Use the Distributive Property.
Simplify within parentheses.
5 Q 5 1 R x2y4
? x2y4
You can name a polynomial based on its degree or the number of monomials it contains.
Number
of Terms
Name Using
Number of Terms
Constant
1
Monomial
1
Linear
2
Binomial
4x2  7x  3
2
Quadratic
3
Trinomial
2x3
3
Cubic
1
Monomial
8x4  2x3  3x
4
Fourth degree
3
Trinomial
Polynomial
Degree
6
0
5x  9
Name Using
Degree
227
Lesson 8-1
Problem 3 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.
Relate
greatest
lesser
least
+
+
degree term
degree term
degree term
∙
Write
∙
18. In standard form, the polynomial 2x 2 3 1 8x2 is .
19. Circle the best name for the polynomial based on its degree.
constant
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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.
_____________________________________________________________________________________
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 (212x 3) 1 (
1 14x 2) 1 (
5
2
1
2 14x) 1 (
1
23. The polynomial
models the number of
pounds, in millions, consumed in the U. S. during the 6-yr period.
Chapter 8
1 1545)
228 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Problem 4 Adding Polynomials
Problem 5 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
m3 1 m2 1 m 2 )
24m3 1 m2 2
m 1
m3 2 m2 2 m 1 Rewrite the subtraction.
m2 2 m 1
Add each pair of terms.
2( 2 24m3 1 9
0 is the coefficient of each missing term.
Line up like terms.
9
25. Write the simplified form of (24m3 2 m 1 9) 2 (4m2 1 m 2 12).
Lesson Check • Do you UNDERSTAND?
Vocabulary Name the polynomial 5x2 1 2x 1 1 based on its degree and number
of terms.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
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 Math Success
Check off the vocabulary words that you understand.
standard form
classifying a polynomial
cubic
quadratic
Rate how well you can add and subtract polynomials.
Need to
review
0
2
4
6
8
Now I
get it!
10
229
Lesson 8-1