Polynomials and Polynomial
Functions
Definitions
Term:
a number or a product of a number
and
variables raised to a power.
3, 5x 2 ,  2 x, 9 x 2 y
Coefficient: the numerical factor of
each term.
5x 2 ,  2 x, 9 x 2 y
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Constant: the term without a variable.
3,  6, 5, 32
Polynomial: a finite sum of terms of the
form axn, where a is a
real number and n is a whole number.
15 x 3  2 x 2  5
21y 6  7 y 5  2 y 3  6 y
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Polynomials and Polynomial
Functions
Definitions
Monomial: a polynomial with
exactly one term.
2
4
ax ,
2x ,
rt ,
2
9m,
9x y
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Binomial: a polynomial with
exactly two terms.
x  8,
5 x  2 x,
2
r  3,
2 x  9 x y
2
Trinomial: a polynomial with
exactly three terms.
x 2  x  8,
5x  2 x  7
2
r  3r  3,
5
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The Degree of a Term with one variable is
the exponent on the variable.
5x  2,
2
2x  4,
9m  1
4
The Degree of a Term with more than one
variable is the sum of the exponents on the
variables.
7x 2 y  3,
2x 4 y 2  6,
9mn5 z 4  10
The Degree of a Polynomial is the greatest
degree of the terms of the polynomial variables.
2 x  3 x  7  3,
3
2 x y  5x y  6 x  6
4
2
2
3
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Practice Problems
Identify the degrees of each term and the degree of the
polynomial.
5x  4 x  5x
2
1
3
3
4𝑎2 𝑏 4 + 3𝑎3 𝑏 5 − 9𝑏 4 + 4
2
8
6
3
0
8
3
4𝑥 5 𝑦 4 + 5𝑥 4 𝑦 6 − 6𝑥 3 𝑦 3 + 2𝑥𝑦
9
1
0
6
1
0
2
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