Aim #86: How do we identify a polynomial by its
terms?
Do Now: State the number of terms in each expression.
1) y2 - 9
2) 7x2 - 4x + 3
3) 2a2 + 6a + 8b - 10a
4) x3y - 3xy + 7y - 5
Polynomials
A polynomial is a numerical expression, variable symbol, or
the sum (or difference) of two or more terms.
Examples:
Type of
Expression
Definition polynomial with 1
Monomial
(mono means "one")
term
Binomial
(bi means "two")
polynomial with
2 terms
(sum of 2
monomials)
polynomial with
3 terms
Trinomial
(tri means "three")
(sum of 3
monomials)
Polynomial
(poly means
"many")
expression with
one or more
terms (sum of
one or more
monomials)
Example Degree of a Polynomial :
1) If the polynomial is a monomial , then the degree is the
sum of the exponents.
a) 4x2 y3
Degree: ______
b) -8x
Degree: ______
c) -3
Degree: ______
2) The degree of a polynomial is the degree of the monomial term with the highest
degree.
a) 6y3 - 10y + 7
Degree: ______
b) 5xy3 - 4x2 y3
Degree: ______
Standard form: arranging the terms starting with the highest
degreed monomial term and continuing in descending order
Ex:
4x2 - 3x3 + 7x - 11 + 2x - 8x4
To identify and then classify a polynomial by its number
of terms, the expression must be simplified first!
Ex:
x2(8x) - 3(3x4 - 1) - 2x3 - 7
a) standard form:
b) degree:
c) leading term: term of highest degree
d) leading coefficient: coefficient of term with
highest degree
e) constant term: term with no variables
Sum it UP, Ms. C!
A ____________________ is the sum (or difference) of monomials.
The degree of a monomial is the ________ of the exponents of the
variable symbols that appear in the monomial.
The degree of a polynomial is the degree of the monomial term with the
_____________ degree.
Quiz Friday, April 22nd
Aims #85-87