# Polynomials Flashcards

1
Q

Degree of a polynomial is…

A

Degree of a polynomial = highest power

2
Q

A polynomial of a degree 3 is..

A

A polynomial of a degree 3 is a cubic

3
Q

A polynomial of a degree 4 is

A

A polynomial of a degree 4 is a quadratic

4
Q

Coefficient is ..

A

the number in front of x term

5
Q

Functions of the type

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

A

is an example of a quadratic

6
Q

Functions of the type

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

A

is an example of a cubic

7
Q

A

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

8
Q

Real and distinct roots is shown..

A

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

9
Q

Equal roots is shown..

A

b^2 -4ac = 0

10
Q

No real roots is shown…

A

b^2 -4ac < 0

11
Q

Steps for evaluating a polynomial

A
1. Completing the square
f(x) = a(x + b)^2 + c
2. find factor for the completing the square table
3. any missing power should assigned coefficient 0
4. factorise
12
Q
```Factor Theorem ( remainder theorem )
x = ? and is a \_\_\_\_
if \_\_\_ = \_\_\_```
A
```x = a is a factor of f(x)
if f(a) = 0```
13
Q

steps for graphs of polynomial functions

A
1. Completing the square
f(x) = a(x + b)^2 + c
2. find factor for the completing the square table
3. any missing power should assigned coefficient 0
4. factorise
5. roots
14
Q

To solve a quadratic inequality. You need to …

A
1. 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
15
Q

The value of k

A

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

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

16
Q

Complete the square of this equation

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

A

f(x) =2x2 + 4x + 3
f(x) =2(x + 1)^2 - 2 + 3
f(x) =2(x + 1)^2 + 1