March 28, 2016
Section 5.3: Polynomials!
A term is a number or the product of a number and one or more
variables.
The numerical factor of a term is called the coefficient.
TERM
COEFFICIENT
-1.2 x5
x3y
-z
2
x9/7
If a term has only a number, it is called a constant.
2, 15, -1, etc
A polynomial is a sum of terms where all of the variables have nonnegative integer powers.
POLYNOMIALS
4x5y + 7xz
3
-5x + 2x + 2/3
NOT POLYNOMIALS
5x-3 + 2x
2
6/x - 5x + 1
March 28, 2016
3x4 - 4x2 + x - 7
For the term 3x4, the 3 is called the ________________
For -4x2 , _______________________
What about the term x? _____________________
The final term in the polynomial is -7 and this term is called a
___________________________
(Notice that we are switching from the subtraction to adding the
negative of the following term. That was how we defined a
polynomial (the sum of terms).)
Do you know what mono, bi, tri and poly mean?
Mono is 1, monogamy: one partner.
Bi is two, a bicycle has two wheels.
Tri is three, and poly is a vague “many”.
Monomial has _______ term: 3x
2
4
Binomial has ________ terms: x + 2
x2 - 4
-x
6
72x5 - 81
Trinomial has _________ terms: 2x2 - 4x + 8
It is good practice to write a polynomial in descending order.
It makes it easier to talk about the degree of a polynomial.
The degree of a term is the value of the exponent for that term.
The degree of a polynomial is the degree of whichever term has the
highest degree.
The coefficient of the term with the highest degree is called the
leading coefficient.
Term
Degree
March 28, 2016
If you have a polynomial that is not in one variable.
Something like: 3x4y3 + 4x2y3 - 7xy + 8
To get the degree of each term you add up the exponents of the
variables in the term.
Term
3x4y3
Degree
4x2y3
- 7xy
8
The degree of the polynomial: __________
Enough of the vocabulary! What can we do with a polynomial?
Polynomials are expressions, not equations.
So, we cannot solve a polynomial unless we set it equal to something
like another polynomial.
We can simplify, add, and subtract polynomials by combining like
terms.
March 28, 2016
To multiply a monomial by a binomial or longer polynomial, we use
the distributive property:
To multiply a binomial by another binomial or longer polynomial, we
can use the distributive property and multiply each term of the first
polynomial by each term of the second polynomial.
March 28, 2016
March 28, 2016
Homework Quiz 4: 7.1, 7.2, 7.3
Open Note
Closed Book
Yes Calculator
No Partner
Sec 7.1 # Sec 7.2 # Sec 7.3 #