Ch.7 Algebraic methods

Question 1

what are the main 2 steps when simplifying an algebraic fraction?

Answer 1

1 - factorise the numerator and denominator where possible
2 - cancel common factors

Question 2

what is a polynomial?

Answer 2

an expression (algebraic or numerical) with positive integer indicies

Question 3

what does the factor theorem state?

Answer 3

if ( x ± p ) is a factor of a polynomial then -p substituted in will equal 0

Question 4

what does ≡ mean?

Answer 4

the 2 expressions are mathematically identical

Question 5

what are the 3 main types of mathematical proof?

Answer 5

proof by
- deduction
- exhaustion
- contradiction

Question 6

how do you prove a mathematical statement is true by deduction?

Answer 6

using logic and algebra

Question 7

how can you prove a mathematical statement is true by exhaustion?

Answer 7

breaking the statement into smaller cases and proving each one

Question 8

how can you prove a mathematical statement is false by contradiction?

Answer 8

by using one counter example to disprove the statement