Polynomials

Question 1

Degree of a polynomial is…

Answer 1

Degree of a polynomial = highest power

Question 2

A polynomial of a degree 3 is..

Answer 2

A polynomial of a degree 3 is a cubic

Question 3

A polynomial of a degree 4 is

Answer 3

A polynomial of a degree 4 is a quadratic

Question 4

Coefficient is ..

Answer 4

the number in front of x term

Question 5

Functions of the type

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

Answer 5

is an example of a quadratic

Question 6

Functions of the type

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

Answer 6

is an example of a cubic

Question 7

Discriminant of a quadratic is…

Answer 7

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

Question 8

Real and distinct roots is shown..

Answer 8

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

Question 9

Equal roots is shown..

Answer 9

b^2 -4ac = 0

Question 10

No real roots is shown…

Answer 10

b^2 -4ac < 0

Question 11

Steps for evaluating a polynomial

Answer 11

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

Question 12

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

Answer 12

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

Question 13

steps for graphs of polynomial functions

Answer 13

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

Question 14

To solve a quadratic inequality. You need to …

Answer 14

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

Question 15

The value of k

Answer 15

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

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

Question 16

Complete the square of this equation

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

Answer 16

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