# Polynomials Flashcards

Degree of a polynomial is…

Degree of a polynomial = highest power

A polynomial of a degree 3 is..

A polynomial of a degree 3 is a cubic

A polynomial of a degree 4 is

A polynomial of a degree 4 is a quadratic

Coefficient is ..

the number in front of x term

Functions of the type

f(x) = 3x^4 + 2x^3 + 2x +x + 5

is an example of a quadratic

Functions of the type

f(x) = 2x^3 + 2x +x + 5

is an example of a cubic

Discriminant of a quadratic is…

Discriminant of a quadratic is = b^2 -4ac

Real and distinct roots is shown..

Real and distinct roots = b^2 -4ac > 0

Equal roots is shown..

b^2 -4ac = 0

No real roots is shown…

b^2 -4ac < 0

Steps for evaluating a polynomial

- Completing the square

f(x) = a(x + b)^2 + c - find factor for the completing the square table
- any missing power should assigned coefficient 0
- factorise

Factor Theorem ( remainder theorem ) x = ? and is a \_\_\_\_ if \_\_\_ = \_\_\_

x = a is a factor of f(x) if f(a) = 0

steps for graphs of polynomial functions

- Completing the square

f(x) = a(x + b)^2 + c - find factor for the completing the square table
- any missing power should assigned coefficient 0
- factorise
- roots

To solve a quadratic inequality. You need to …

- sketch the graph of the related quadratic function

consider which parts of the graph are above x - axis

consider which parts of the graph are below x - axis

The value of k

f (x) = k ( x - a ) ( x - b ) ( x - c )

sub in the coordinates of any other known points on the graph