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5.5 Polynomials
Classic Types of Polynomials
• Monomial: 1 term
• Binomial: 2 terms
• Trinomial: 3 terms
What are Terms???
Items separated by subtraction or addition signs
Polynomials
A Polynomial is a monomial,
or a sum of monomials
5x + 3
3x2 + 2x - 5
abba2
15 23
Binomial
Trinomial
Determine if an expression is a polynomial:
• 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
Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial.
No
32
3
12
1xx
x
Is the term a polynomial? If so, say whether it is a monomial, binomial, or trinomial.
YES, trinomial since it has 3 terms
Numeric factor of a term is called the coefficient.
935 24 xx
Identify the terms and Give the coefficient of each term.
94 6 1m m 9: 4 ,6 , 1terms m m : 4,6, 1coefficients
Identify the terms and Give the coefficient of each term.
8 6 6 6 4 7 82 8 4x y x y x y xy 8 6 6 6 4 7 8: , 2 ,8 , 4terms x y x y x y xy
:1, 2,8, 4coefficients
To simplify by collecting “like terms”
“like terms” have the same exact variables to the same exact power. Only the coefficients may be different.
5 51 15 2
4 2x x x
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
= (3 – 1)x5y4
= 2x5y4 - 4y4
y4+(– 6 + 2)
Simplify by collecting like terms:
2m4 – 4m3 + 3m3 – 1
2m4 – m3 – 1
Simplify by collecting like terms:3x5y4 – 6y4 + m3 – x5y4
2x5y4 – 6y4 + m3
The Degree of a term is the sum of the exponents of the variables.
9th
deg4th
deg
3rddeg
Simplify by collecting like terms:3x5y4 – 6y4 + m3 – x5y4
2x5y4 – 6y4 + m3
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.
This is a 9th degree polynomial.
Identify the degree of each term and the degree of the polynomial.
- 63x2y3 – 16xy5 + y4
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.
This is a 6th degree polynomial.
5th
deg6th
deg4th
deg
Identify the degree of each term and the degree of the polynomial.
9x6y5 – 7x4y3 + 3xy4
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.
This is a 11th degree polynomial.
11th
deg7th
deg5th
deg
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
(2-52 even, 53)
