Opener: 1.) Find all solutions to the following equation:
10x3 + 8x2 = 0
Complete each of
problems in your
2.) Factor out the GCF of the following expression:
10x4y ‐ 18x2
3.) Write each expression as a product of expressions:
3b2 ‐ 15b + b ‐ 5
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.
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
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
Basic Arithmetic with
Polynomials Expand each expression. Combine like terms to get a
*Like terms: same variables
& same exponents
2 3 2
(Ex. 7 ) 3x ‐7x+1‐2(10x ‐x +3x)
(Ex. 8 ) (3x‐1)(x +2x+5)
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
The degree of the sum of two nonzero polynomials is...