5.5 Polynomials
• Goals:
1. To identify terms, coefficients, and
factors of a term.
2. To simplify a poly by collecting like terms
3. To identify the degree of the poly
Mono__________________
Bi______________________
Tri_____________________
Poly______________________
Monomial  Polynomials
A Polynomial is a monomial,
or a sum of monomials
3x2 + 2x - 5
5x + 3
1
 5a b  ab
2
Trinomial
3 2
Binomial
To determine if an expression is a
polynomial:
First check that every term is a
monomial. If every term is a
monomial then the expression is a
polynomial
Is the term a polynomial? If so, say whether it
is a monomial, binomial, or trinomial.
y2 + 2y
Binomial, since it has
two TERMS
“terms” are added,
“factors” are multiplied
Is the term a polynomial? If so, say whether it
is a monomial, binomial, or trinomial.
1
1 3
2
 2x  x
x
3
No
“terms” are added,
“factors” are multiplied
Is the term a polynomial? If so, say whether it
is a monomial, binomial, or trinomial.
5 x  3x  9
4
2
YES, trinomial since
it has 3 terms
Numeric factor of a term is
called the coefficient.
To simplify by collecting
“like terms”
“like terms” have the same exact
variables to the same exact power.
Only the coefficients may be different.
7m2 – 2m2 = (7 – 2)m2
= 5m2
To simplify by collecting
“like terms”
“like terms” have the same exact
variables to the same exact power.
Only the coefficients may be different.
3x5y4 – 6y4 – x5y4 + 2y4
4
5
4
+(–
6
+
2)
y
= (3 – 1)x y
= 2x5y4 - 4y4
Simplify by collecting like terms:
2m4 – 4m3 + 3m3 – 1
2m4 – m3 – 1
Simplify by collecting like terms:
3m5 – 3m2 + m – 1
(no like terms)
Simplify by collecting like terms:
3x5y4 – 6y4 + m3 – x5y4
2x5y4 – 6y4 + m3
9th
deg
4th
deg
3rd
deg
The Degree of a term is the sum of
the exponents of the variables.
Simplify by collecting like terms:
3x5y4 – 6y4 + m3 – x5y4
2x5y4 – 6y4 + m3
This is a 9th degree
polynomial.
The Degree of a term is the sum of
the exponents of the variables.
The Degree of a polynomial is
the highest degree of any term.
Identify the degree of each term and the
degree of the polynomial.
- 63x2y3 – 16xy5 + y4
5th
deg
6th
deg
4th
deg
This is a 6th degree
polynomial.
The Degree of a term is the sum of
the exponents of the variables.
The Degree of a polynomial is
the highest degree of any term.
Identify the degree of each term and the
degree of the polynomial.
9x6y5 – 7x4y3 + 3xy4
11th
deg
7th
deg
5th
deg
This is a 11th degree
polynomial.
The Degree of a term is the sum of
the exponents of the variables.
The Degree of a polynomial is
the highest degree of any term.
9x6y5 – 7x4y3 + 3xy4
• Leading term is the term that has the
highest degree in the poly
• Ex: 9x6y5
• Leading coefficient is the coefficient of the
leading term.
• Ex: 9
Assignment:
Page 224
6-46 even