1. C2: Chapter 1 Algebra and Functions Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 1 st September 2015

2. Terminology dividend divisor quotient remainder ? ? ? ?

3. 4 2 3. 0 0 0 0 11 3 3 9 3 8. 8 8 5 0 1. We found how many whole number of times (i.e. the quotient) the divisor went into the dividend. 2. We multiplied the quotient by the dividend. 3. …in order to find the remainder. 4. Find we ‘brought down’ the next number. Normal Long Division

4. x + 56x 3 + 28x 2 – 7x + 15 6x 2 6x 3 + 30x 2 – 2x 2 – 7x - 2x – 2x 2 – 10x 3x + 15 + 3 3x + 15 0 The Anti-Idiot Test: You can check your solution by finding (x+5)(6x 2 – 2x + 3) The Anti-Idiot Test: You can check your solution by finding (x+5)(6x 2 – 2x + 3)

5. x - 13x 3 – 3x 2 – 4x + 4 3x 2 3x 3 – 3x 2 0 – 4x + 4 + 0 – 4x + 4 0 – 4

6. x - 42x 3 – 5x 2 – 16x + 10 2x 2 2x 3 – 8x 2 3x 2 – 16x + 3x 3x 2 – 12x -4x + 10 – 4 -4x + 16 -6 Find the remainder. Q: Is (x-4) a factor of 2x 3 – 5x 2 – 16x + 10?

7. Exercises 1a 1i 2a 2i 2b ? ? ? ? ?

8. Divide x 3 – 1 by x – 1 How would we write the division? Dividing polynomials with ‘missing’ terms ?

9. Divide x 4 – 16 by (x+2) Dividing polynomials with ‘missing’ terms ?

10. 8 3 =2 + 1 3 dividend divisor quotient remainder Recap

11. So what does f(a) equal? Remainder and Factor Theorem

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13. Basic Examples ? ? ? ?

14. Show that (x – 2) is a factor of x 3 + x 2 – 4x - 4 Examples ?

15. Fully factorise 2x 3 + x 2 – 18x – 9 Tip: If f(x) = 2x 3 + x 2 – 18x – 9, then try f(-1), f(1), f(2), etc. until one of these is equal to 0. Examples ?

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17. C2 May 2013 (R) ? ?

18. Exercise 1D Q1, 2, 4, 6, 8, 10 Examples

19. Recap ?

20. Bro tip: think what you could make x in order to make the factor (2x-1) zero. Recap ?

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22. Le Exercise 1E: Q1f, g, h, i 2, 4, 6, 8, 10 Le Exercise 1F 4, 5, 8, 10, 15. Exercises