Ch.7 Algebraic methods Flashcards
what are the main 2 steps when simplifying an algebraic fraction?
1 - factorise the numerator and denominator where possible
2 - cancel common factors
what is a polynomial?
an expression (algebraic or numerical) with positive integer indicies
what does the factor theorem state?
if ( x ± p ) is a factor of a polynomial then -p substituted in will equal 0
what does ≡ mean?
the 2 expressions are mathematically identical
what are the 3 main types of mathematical proof?
proof by
- deduction
- exhaustion
- contradiction
how do you prove a mathematical statement is true by deduction?
using logic and algebra
how can you prove a mathematical statement is true by exhaustion?
breaking the statement into smaller cases and proving each one
how can you prove a mathematical statement is false by contradiction?
by using one counter example to disprove the statement