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Algebra
Chapter 8 – Section 4
Polynomials
Polynomial: a monomial or a sum of monomials
Monomial: a number, a variable, or a product of numbers and variables
Binomial: the sum of two monomials
Trinomial: the sum of three monomials
Expression
2x – 3yx
8n  5n
3
2
-8
4a  5a  a  9
2
Polynomial?
Yes. 2x – 3yz = 2x + (-3yz). The expression is the
sum of two monomials.
No. 5n
2

5
2 , which is not a monomial. You
n
cannot have a variable in the denominator.
Yes. –8 is a real number.
2
Yes. The expression simplifies to 4a  6a  9, so it
is the sum of three monomials.
Monomial, Binomial, or
Trinomial?
Binomial
None of these.
Monomial
Trinomial
Examples: State whether each expression is a polynomial. If it is a polynomial, identify
it as a monomial, binomial, or trinomial.
a. 6 – 4 = yes, binomial
2
b. x  2xy  7 = yes, trinomial
14d  19e 2
 no (variable in the denominator)
c.
4
5d
Degree of a monomial: the sum of the exponents of its variables
Degree of a polynomial: the greatest degree of any term in the polynomial.
*To find the degree of a polynomial you must find the degree of each of its terms.
Examples: Find the degree of each polynomial.
2
a. 12  5b  6bc 8bc = degree of 3
2
b. 9x  2x  4 = degree of 2
2 5
c. 14g h i = degree of 8
Writing polynomials in order: The terms of a polynomial are usually arranged so that
the powers of one variable are in ascending (increasing) order or descending
(decreasing) order.
Examples: Arrange the terms of the polynomial so that the powers of x are in
2
3
3
2 2
4 4
descending order and then ascending order. 7y  4x  2xy  x y  6x y
2
3
2 2
3
4 4
Ascending: 7y  2xy  x y  4x  6x y
4 4
3
2 2
3
2
Descending: 6x y  4x  x y  2xy  7y