16/1/12 Lesson Summary

By Jemima

Remainder Theorem
- Used to find the remainder
- 0 isn't a remainder, if you get a 0, it would be factor theorem

Worksheet A01B (Polynomials)
Question 1: State whether the function is a polynomial, then explain why or why not

Question 2: Exapnd whenever necessary
                   There are 2 methods that can be used to solve the questions
Method 1
2x^2+3x≣(A-2)x^2+(B-1)x
2=A-2          3=B-1
A=4             B=4

or

Method 2
If x=1
5=A-2+B-1
A+B=8

Question 3: for (b) and (c) is not an identity.
                    The way to write the conclusion: Since there are multiple values of A, B and C, ∴the
                    above is not an identity.

Question 4:
x^3+7x^2+ax-5 -> Dividend
(x^2+x-2) -> Divisor
f(x) -> Quotient
(x-1)(bx-1) -> Remainder

(2x^3+4x^2-5)/(x-1)(x+2)=2x+6+1/(x-1)
Sub x=1 for A; Sub x=-2 for B

f(x)=(x^3+4x^2-6)/(x+3)(x-1), x≠-2 or 1
∴ The above is not a function as an asymptote would be encountered.

Homework
- Redo Worksheet A01A (Functions)
- Read and understand the chapter on remainder theorem
- Complete practice 7 on page 52