1. 10: Polynomials © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

2. Polynomials Module C1 "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3. Polynomials 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

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

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

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

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

8. Polynomials Expand the brackets in the following: Answer: Solution: Exercise

9. Polynomials 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.

10. Polynomials Factorise fully the following cubic: Solution: Exercise

11. Polynomials

12. 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.

13. Polynomials 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

14. Polynomials 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 1 st pair of brackets by each of the 2 terms in the 2nd

15. Polynomials 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.