1. Lucan Community College Leaving Certificate Mathematics
Higher Level
Mr Duffy
Polynomials & Cubic Factors
© Ciarán Duffy

2. The following are examples of Polynomial Functions:
A quadratic polynomial
A cubic polynomial
A quartic polynomial
Polynomials only contain terms of the type ,
where n is a positive integer

3. Expanding Cubic Functions
We multiply 2 of the parts together first, leaving the third unchanged
e.g. 1

4. Expanding Cubic Functions
We multiply 2 of the parts together first, leaving the third unchanged
e.g. 1
Now multiply each of the 3 terms in the 1st pair of brackets by each of the 2 terms in the 2nd

5. Expanding Cubic Functions
We multiply 2 of the parts together first, leaving the third unchanged
e.g. 1
Now multiply each of the 3 terms in the 1st pair of brackets by each of the 2 terms in the 2nd

6. Expanding Cubic Functions
We multiply 2 of the parts together first, leaving the third unchanged
e.g. 1
Now multiply each of the 3 terms in the 1st pair of brackets by each of the 2 terms in the 2nd

7. Exercise
Expand the brackets in the following:
Solution:
Answer:

8. Factorising Simple Cubics
Some cubic functions which contain a common factor can be factorised by inspection.
( Others are best done using the Factor Theorem
which is covered later ).
e.g. Factorise fully the following:
Solution:
Common factor:
We must now factorise the quadratic.
Trinomial factors:

9. Exercise
Factorise fully the following cubic:
Solution:

11. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

12. where n is a positive integer
Polynomials only contain terms of the type ,
where n is a positive integer
The following are examples of Polynomial Functions:
Polynomial Functions
A quadratic polynomial
A cubic polynomial
A quartic polynomial

13. Expanding Cubic Functions
e.g. 1
We multiply 2 of the parts together first, leaving the third unchanged
Now multiply each of the 3 terms in the 1st pair of brackets by each of the 2 terms in the 2nd

14. Factorising Simple Cubics
e.g. Factorise fully the following:
Common factor:
Solution:
( Others are best done using the Factor Theorem
which is covered later ).
Some cubic functions which contain a common factor can be factorised by inspection.
Trinomial factors:
We must now factorise the quadratic.