1) The document defines polynomials as expressions that can be written as the sum of one or more monomials. A monomial is the product of a number, variable, and nonnegative integer powers. 2) The degree of a monomial is the sum of the exponents of its variables. The degree of a polynomial is the highest degree among its monomial terms. 3) Polynomials are classified by degree, with linear having degree 1, quadratic degree 2, cubic degree 3, and so on. Basic arithmetic with polynomials involves combining like terms.

1. Opener: 1.) Find all solutions to the following equation:
10x3 + 8x2 = 0
Complete each of
the following
problems in your
notes.
2.) Factor out the GCF of the following expression:
10x4y ‐ 18x2
3.) Write each expression as a product of expressions:
3b2 ‐ 15b + b ‐ 5
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2. Homework
Questions:
2

3. 7.6 Anatomy of a Polynomial
Topic One: Examine the examples of polynomials below. What do
Defining a Polynomial you think a polynomial is? Write down how you think
you might define one.
x2‐1 3x+5y+1 2x3‐9x4‐3x+2 y2‐x3‐xy
x x3‐8x2+1 3
Polynomial: an expression that you write as the sum of
one or more monomials.
Monomial: Product of a number, coefficient, and one
more variable raised to nonnegative integer powers.
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4. Topic Two:
Degree of a Degree of a Monomial:
Monomial • One Variable: exponent of the variable
(Ex. 1 & 2) 5x2 5
• >One Variable: sum of the exponents of each variable
(Ex. 3 & 4) 5x2y3 x2(x3y5)
It's Your Turn!!!
Name the coefficient, variable, and degree of each
monomial.
3x2
‐4a5
b3
‐.5
7x3y5
4

5. Topic Three:
Classifying Degree of a Polynomial: Largest degree among all the
Polynomials monomials in the polynomial.
(Ex. 5 & 6)
Naming a Polynomial:
Degree Type of Polynomial
1 linear
2 quadratic
3 cubic
4 quartic
5 quintic
5

6. Topic Four:
Basic Arithmetic with
Polynomials Expand each expression. Combine like terms to get a
polynomial answer.
*Like terms: same variables
& same exponents
2 3 2
(Ex. 7 ) 3x ‐7x+1‐2(10x ‐x +3x)
2
(Ex. 8 ) (3x‐1)(x +2x+5)
6

7. Topic Four:
Basic Arithmetic with Use the following polynomials to help you complete
Polynomials the statements below.
x2+4x+5 ‐2x5+7x‐1 3x+7 14x 9
The degree of a product of two nonzero polynomials
is....
The degree of the sum of two nonzero polynomials is...
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8. Homework: • Polynomial Worksheet
• Mini Writing # 1
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9. 9