## Wednesday, 6 February 2013

### Lesson Summary 6th Feb - Wednesday ; Kaelan

Practice 1:

1 = A(x+2) + B(x+1)
1 = (A+B)x + 2A + B

Compare Co-efficients. A+B = 0
2A+B=1
Therefore:  A = 1; B = -1

1             1
------   -   ------
(x+1)      (x+2)

b) Simple:

9x+9                 9(x+1)                 9
--------------- =  -----------------  =  --------
(x+1)(x-2)          (x+1)(x-2)          (x-2)

c) 3x+5 = A(x+2)(x+3) + B(x+1)(x+3) + C(x+1)(x+2)

Sub x = -1

2 = 2A
A = 1

Sub x = -2, -1 = -B, B = 1
Sub x = -3, -4 = 2C, C = -2

Therefore :    1                      1                    2
-------------   +  -------------   -  ------------
(x+1)               (x+2)              (x+3)

Practice 2 :

1 = Ax(x-1) + B(x-1) + Cx^2 OR        1=(Ax+B)(x-1)+Cx^2
1 = (A+C)x^2 + (B-A)x -B OR     x=1, C=1
Compare Coefficients OR       x=0, B=-1
B=-1 OR        x=-1, A = -1
A =-1
C = 1

A question :

x^2
------------------
9-x^2

Long divide to give :  -1 + 9/9-x^2
= -1  + 9/(3+x)(3-x)
9 = A(3-x) + B(3+x)
x=3 , B=1.5
x=-3, A=1.5

-1 + 3/(6-2x) + 3/(6+2x)

NOTE: ALWAYS FACTORISE, A NON FACTORISED POLYNOMIAL WILL NOT WORK. have fun in a loop.