Download Polynomials

Polynomials
Monomial: a number or a product of numbers and variables with whole number exponents
Degree of a Monomial: the sum of the exponents of the variables
Polynomial: an expression of two or more algebraic terms
Binomial: a polynomial with two terms
Trinomial: a polynomial with three terms
Degree of a Polynomial: given by the term with the greatest degree
Standard Form: the form of a polynomial when its terms are written in descending order by
degree
Leading Coefficient: the coefficient of the first term of a polynomial written in standard form
Polynomials
Identify the degree of each monomial.
1. x2
2. 3
3. a2b2
4. 7x
5. 4x2
6. 2x5
7. 6x2
8. 3p3m4
9. 2x8y3
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and
number of terms.
Polynomial
10. 2x2 + x3 – 7x + 1
11. 5 – 3x + 4x2
12. 6 + 7x – 4x3 + x2
13. x2 – 3 + 2x5 + 7x4 – 12x
14. 5x3 + 2x – 1 – 10x2 + 9x5 – 3x4
15. 2x + x3 – x2 – 5
16. 5x2 + 3x4 – x
17. 6x3 + 7x5
18. -3x2 + x4 – x – 2x3 + 8
Standard Form
Leading
Coefficient
Degree
# of Terms
Polynomials KEY
Identify the degree of each monomial.
1. x2
2
2. 3
0
3. a2b2
4
4. 7x
1
5. 4x2
2
6. 2x5
5
7. 6x2
2
8. 3p3m4
7
9. 2x8y3
11
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and
number of terms.
Standard Form
Leading
Coefficient
Degree
# of Terms
x3 + 2x2 – 7x + 1
1
3
4
4x2 – 3x + 5
4
2
3
-4x3 + x2 + 7x + 6
-4
3
4
13. x2 – 3 + 2x5 + 7x4 – 12x
2x5 + 7x4 + x2 – 12x – 3
2
5
5
14. 5x3 + 2x – 1 – 10x2 + 9x5 – 3x4
9x5 – 3x4 + 5x3 – 10x2 + 2x – 1
9
5
6
x3 – x2 + 2x – 5
1
3
4
3x4 + 5x2 – x
3
4
3
7x5 + 6x3
7
5
2
x4 – 2x3 – 3x2 – x + 8
1
4
5
Polynomial
10. 2x2 + x3 – 7x + 1
11. 5 – 3x + 4x2
12. 6 + 7x – 4x3 + x2
15. 2x + x3 – x2 – 5
16. 5x2 + 3x4 – x
17. 6x3 + 7x5
18. -3x2 + x4 – x – 2x3 + 8