6.1 Polynomial Functions

Monomial – an expression that is either a variable, a real number or the product of a real number and variables with whole number exponents.

Polynomial – a monomial or the sum of monomials

Degree – the sum of the exponents of a term

Always put answers in standard form – descending order of exponents

Classifying a PolynomialClassifying a Polynomial

By Degree 0 – constant 1 – linear 2 – quadratic 3 – cubic 4 – quartic 5 - quintic

By # of Terms 1 – monomial 2 – binomial 3 – trinomial 4 or more -

polynomial

EX 1

Classify: 9 + x3

EX 2

Classify: x3 – 2x2 – 3x4

EX 3

Write in standard form and classify: p(p – 5) + 6

EX 4

Write in standard form and classify: (x + 1)(x – 2)(x + 3)(x – 4)

Notes 6.2 Polynomial & Linear Factors

EX 1

Write in factored form: 3x3 - 18x2 + 24x

Zeros = Roots = Solutions = X-intercepts

EX 2

Find the zeros and graph: y = (x + 1)(x – 1)(x + 3)

EX 3

Find the zeros and graph: y = (x – 7)(x – 5)(x – 3)

EX 4

Write an equation in standard form with zeros at 2, -3, 0.

If a linear factor of a polynomial is repeated then the zero is repeated – multiple zero.

A multiple zero has a multiplicity equal to the number of times the zero occurs.

EX 5

Find any multiple zeros and state the multiplicity.

f(x) = x5 – 6x4 + 9x3

Equivalent Statements about Polynomials

1. -4 is a solution of x2 + 3x – 4 = 0

2. -4 is an x-intercept of the graph y = x2 + 3x – 4

3. -4 is a zero of y = x2 + 3x – 4

4. x + 4 is a factor of x2 + 3x - 4