Algebraic Methods Flashcards
What should you do when simplifying an algebraic fraction
Factorise the numerator and denominator where possible and then cancel common factors
What do you use to divide a polynomial by (x +- p) where p is a constant
You can use long division
If f(x) is a polynomial the factor theorem states what
If f(p) = 0, then (x - p) is a factor of f(x)
If (x - p) is a factor of f(x), then f(p) = 0
What must you do for mathematical proof
State any information and assumptions you are using
Show every step of your proof clearly
Make sure that every step follows logically from the previous step
Make sure you have covered all possible cases
Write a statement of proof at the end of your working
What should you do to prove an identity
Start with the expression on one side of the identity
Manipulate that expression algebraically until it matches the other side
Show every step of your algebraic working
What are the two ways to prove a mathematical statement is true
Deduction and exhaustion
What is the way to prove a mathematical statement is not true
Counter - example
What is deduction
This means starting from known facts or definitions, then using logical steps to reach the desired conclusion
What is exhaustion
This means breaking the statement into smaller cases and proving each case separately
What is counter - example
A counter - example is one example that does not work for the statement. You do not need to give more than one example, as one is sufficient to disprove a statement