6.5 Polynomials
CORD Math
Mrs. Spitz
Fall 2006
Warm-up
Express in scientific notation:
1. 42,345
2. 62,917.6
3. 0.000567
Express in decimal notation.
4. 3.7 x 105
5. 7.0 x 10-6
Warm-up
Express in scientific notation:
1. 42,345
4.2345 x 104
2. 62,917.6 6.29176 x 104
3. 0.000567 5.67 x 10-4
Express in decimal notation.
4. 3.7 x 105 370,000
5. 7.0 x 10-6 .000007
1. Be able to determine the degree of a polynomial.
2. Be able to classify a polynomial.
3. Be able to write a polynomial in standard form.
Assignment
6.5 Practice Worksheet
Show all work. You have a mid-chapter
test on Monday!
Monomial: A number, a variable or the product of a
number and one or more variables.
Polynomial: A monomial or a sum of monomials.
Binomial: A polynomial with exactly two terms.
Trinomial: A polynomial with exactly three terms.
Coefficient: A numerical factor in a term of an algebraic
expression.
Degree of a monomial: The sum of the exponents of all
of the variables in the monomial.
Degree of a polynomial in one variable: The largest
exponent of that variable.
Standard form: When the terms of a polynomial are
arranged from the largest exponent to the smallest
exponent in decreasing order.
What is the degree of the monomial?
4 2
5x b
The degree of a monomial is the sum of the
exponents of the variables in the monomial.
The exponents of each variable are 4 and 2. 4+2 = 6.
The degree of the monomial is 6.
The monomial can be referred to as a sixth degree
monomial.
A polynomial is a monomial or the sum of monomials
4x
2
3x  8
3
5 x  2 x  14
2
Each monomial in a polynomial is a term of the
polynomial.
The number factor of a term is called the coefficient.
The coefficient of the first term in a polynomial is the
lead coefficient.
A polynomial with two terms is called a binomial.
A polynomial with three terms is called a trinomial.
The degree of a polynomial in one variable is the
largest exponent of that variable.
2
A constant has no variable. It is a 0 degree polynomial.
4x 1 This is a 1
st
degree polynomial. 1st degree polynomials are linear.
5 x  2 x  14
2
3x  8
3
This is a 2nd degree polynomial. 2nd degree
polynomials are quadratic.
This is a 3rd degree polynomial. 3rd degree polynomials are
cubic.
Classify the polynomials by degree and number of terms.
Classify by
number of
terms
Polynomial
Degree
Classify by
degree
a.
5
Zero
Constant
Monomial
b.
2x  4
First
Linear
Binomial
c.
3x 2  x
Second
Quadratic
Binomial
Third
Cubic
Trinomial
d.
x  4x 1
3
2
e. 3x4 – 4x3 + 6x2 - 7
Fourth
Quartic
Polynomial
Ascending v. descending order
When you place terms in ascending or
descending order (in x), the degree of y has
no bearing on the placement of terms
UNLESS the degree of x is the same.
x5y3 +x5y2
Even though the degree of x is the same in
both terms, the first term is of degree 8 and
the second term is of degree 7.
To rewrite a polynomial in standard form, rearrange
the terms of the polynomial starting with the largest
degree term and ending with the lowest degree term.
The leading coefficient, the coefficient of the first
term in a polynomial written in standard form, should be
positive.
Write the polynomials in standard form.
5x  4 x 4  x 2  7
2 x3  x 4  7  5x  5x 2
4x  x  5x  7
 x  2x  5x  5x  7
4
2
4
3
2
Remember: The lead
coefficient should be
positive in standard form.
 1( x  2 x  5 x  5 x  7)
To do this, multiply the
polynomial by –1 using
the distributive property.
x 4  2x 3  5x 2 5x  7
4
3
2
Write the polynomials in standard form and identify the
polynomial by degree and number of terms.
1.
7  3x  2 x
2.
1  3x  2 x
3
2
2
7  3x  2 x
3
2
7  3x 3  2 x 2
 3x  2x  7
3
2

 1  3x 3  2 x 2  7

3x 3  2 x 2  7
This is a 3rd degree, or cubic, trinomial.
1  3x  2 x
2
1  3x 2  2 x
3x  2x  1
2
This is a 2nd degree, or quadratic, trinomial.