Chapter 3 Polynomial Functions

Front 1

A function is NOT a polynomial is it contains what characteristics (3)

Back 1

1. roots of a variable (ie. square root of 3x) 2. negative or fractional exponents 3. non real coefficient

Front 2

End behaviour of odd degree polynomial functions that are positive

Back 2

Start in Q3 and end in Q1

Front 3

End behaviour of odd degree polynomial functions that are negative

Back 3

Starts in Q2 ends in Q4

Front 4

Characteristics of odd degree polynomial functions (3)

Back 4

- y intercept is constant term of function

- number of x-intercepts is equal to the degree of the polynomial

- domain and range are elements of real

Front 5

End behaviour of even degree polynomial functions that are positive

Back 5

Starts Q2 ends Q1 (opens up)

Front 6

End behaviour of even degree polynomial functions that are negative

Back 6

Starts Q3 ends Q4 (opens down)

Front 7

Characteristics of even degree polynomial functions (3)

Back 7

- y intercept is constant term

- number of x-intercepts is

- domain is an element of reals and range depends on max/min

Front 8

what is a remainder

Back 8

amount left over from division

Front 9

Division algorithm/statement (2 options)

Back 9

P(x) = Q(x)D(x) + R(x) or (P(x))/(D(x)) = Q(x) + (R(x))/(D(x))

Front 10

when polynomialsyou must make sure both dividend and divisor are written in ______ order of powers

Back 10

descending

Front 11

Remainder Theroem

Back 11

When a polynomial P(x) is divided by a binomial x-a the remainder is P(a)

Front 12

Factor Theorem

Back 12

The binomial x-a is a factor of the polynomial function P(x) if and only if P(a) = 0

Front 13

How to factor an integral polynomial with a leading coefficient of 1

Back 13

- determine factors of constant term (these will be your possible factors)

- test using remainder theorem, if = 0, it is a factor

- use that factor and divide P(x) to create new polynomial

- test again (repeat)

Front 14

How to factor an integral polynomial function with a leading coefficient other than 1

Back 14

- take factors of constant term first

- take factors of leading coefficient

- possible factors for the polynomial will be a combination of both (a/b) -> (constant term/leading coefficient)

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Front 15

The ___ of a function, the ______ of the graph of the function and the ____ of the corresponding equation y = 0 are the ______ number

Back 15

zeros, x-intercept, roots, same

Front 16

Multiplicity

Back 16

multiplicity of a zero corresponds to the number of times a zero occurs

Front 17

If the graph passes straight through the x-axis the zero has a multiplicity of

Back 17

one

Front 18

if the graph is tangent to the x-axis the zero has a multiplicity of

Back 18

two

Front 19

if the graph has a point of inflection on the x-axis the zero has a multiplicity of

Back 19

three

Front 20

When determining the equation of a polynomial function given its graph

Back 20

find (x-intercepts)/roots and substitute a point from the graph to determine V.S or reflection