DATE
NAME
9-4
Student Edition
Pages 514–519
Study Guide
Polynomials
A polynomial is a monomial or a sum of monomials. A binomial
is the sum of two monomials, and a trinomial is the sum of three
monomials.
The degree of a monomial is the sum
of the exponents of its variables.
Examples of each type of polynomial
are given in the following chart.
Monomial
Binomial
Trinomial
Monomial
Degree
5x
4 abc
3x 1 2
4 x 1 5y
5x 2 2x 1 7
a 2 1 2ab 1 b 2
5x
4ab 3c 4
2
1131458
2
2
2
To find the degree of a polynomial, first find the degree of each
of its terms. The degree of the polynomial is the greatest of the
degrees of its terms. The terms of a polynomial are usually
arranged so that the powers of one variable are in either
ascending or descending order.
Ascending Order: 3 1 5a 2 8a2 1 a3
Descending Order: (in x) x 5 y2 2 x 4 1 x 3 y2 1 5xy
Find the degree of each polynomial.
1. 4x 2 y 3 z
2. 22abc
3. 15m
4. s 1 5t
5. 22
6. 18x 2 y 1 4yz 2 10y
7. x4 2 6x 2 2 2x 3 2 10
8. 2x 3 y 2 2 4xy 3
9. 22r 8 s 4 1 7r 2 s 2 4r 7 s 6
Arrange the terms of each polynomial so that the powers of x
are in descending order.
10. 24x 2 y 2 12x 3 y 2 1 6x 4
11. 20x 2 10x 2 1 5x 3
12. 9bx 1 3bx 2 2 6x 3
13. 215x 3 1 10x 4 y 2 1 7xy 2
14. ax 2 1 8a 2 x 5 2 4
15. x5 1 x2 2 x3
Arrange the terms of each polynomial so that the powers of x
are in ascending order.
16. x4 1 x3 1 x2
17. 2x3 2 x 1 3x7
18. 25cx 1 10c 2 x 3 1 15cx 2
19. 3 1 9x 4 1 9x 3
20. 24nx 2 5n 3 x 3 1 5
21. 4xy 1 2y 1 5x 2
© Glencoe/McGraw-Hill
64
Algebra 1
9-4
DATE
NAME
Student Edition
Pages 514–519
Practice
Polynomials
Find the degree of each polynomial.
1. 5a 2 2b2 1 1
2. 4a3 2 2a
3. x 1 3x4 2 21x2 1 x3
4. b 1 6
5. 24xy 2 xy3 1 x2
6. n3 1 m2 1 n2m2
7. 32r4
8. 8x2 2 2x8
9. 22x2y 1 3xy3 1 x3
10. 10s2t2 1 4st2 2 5s3t2
Arrange the terms of each polynomial so that the powers of x
are in ascending order.
11. 5 1 2x2 1 x4 1 3x3
12. 3x 1 1 1 2x2
13. 5x 2 6 1 3x2
14. 9x2 1 2 1 x3 1 x
15. 23 1 3x3 2 x2 1 4x
16. x2 1 x4 2 2x 2 x3
17. 6x2 1 6 1 x3 1 12x
18. 7r5x 1 21r4 2 r2x2 2 15x3
Arrange the terms of each polynomial so that the powers of x
are in descending order.
19. x 2 3x2 1 4 1 5x3
20. 1 2 x 1 x2 2 x3
21. x2 1 3x3 1 27 2 x
22. x 1 3x3 2 17 1 x2
23. x 2 1 1 x3
24. x2 1 64 2 x 1 3x3
25. 25 2 x3 1 x
26. 5p 1 p3x2 1 px 1 3 px3
© Glencoe/McGraw-Hill
1
64
Algebra 1