C2: Chapter 1 Algebra and Functions Dr J Frost

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C2: Chapter 1 Algebra and Functions Dr J Frost

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C2: Chapter 1 Algebra and Functions Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 1st September 2015 dividend divisor quotient remainder ? ? ? ? 4 2 3 . 0 0 0 0 11 3 3 3 9 3 8 . 8 8 5 0 x 5 6x3 28x2 7x

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

dividend divisor quotient remainder ? ? ? ?

4 2 3 . 0 0 0 0 11 3 3 3 9 3 8 . 8 8 5 0

x + 5 6x3 + 28x2 – 7x + 15 6x2 6x3 + 30x2 – 2x2 – 7x - 2x – 2x2 – 10x 3x + 15 + 3 3x + 15 0 The Anti-Idiot Test:
You can check your solution by finding (x+5)(6x2 – 2x + 3)

x - 1 3x3 – 3x2 – 4x + 4 3x2 3x3 – 3x2 0 – 4x + 4 + 0 – 4x + 4 0 – 4

x - 4 2x3 – 5x2 – 16x + 10 2x2 2x3 – 8x2 3x2 – 16x + 3x 3x2 – 12x -4x + 10 – 4 -4x + 16 -6 Find the remainder. Q: Is (x-4) a factor of 2x3 – 5x2 – 16x + 10?

1a 1i 2a 2i 2b ? ? ? ? ?

Divide x3 – 1 by x – 1 How would we write the division? ?

Divide x4 – 16 by (x+2) ?

8 3 = 2 + 1 3 dividend divisor quotient remainder

So what does f(a) equal?

! !

? ? ? ?

Show that (x – 2) is a factor of x3 + x2 – 4x - 4 ?

Fully factorise 2x3 + x2 – 18x – 9 Tip: If f(x) = 2x3 + x2 – 18x – 9, then try f(-1), f(1), f(2), etc. until one of these is equal to 0. ?

? ?

C2 May 2013 (R) ? ?

Exercise 1D
Q1, 2, 4, 6, 8, 10

?

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

?

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

C2: Chapter 1 Algebra and Functions Dr J Frost

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