Chapter 7 - Algebraic Methods Flashcards Preview

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Flashcards in Chapter 7 - Algebraic Methods Deck (8)
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1
Q

When simplifying an algebraic fraction what do you do?

A

You factorise the numerator and denominator where possible.

You then cancel out the factors.

2
Q

What are the steps for polynomial division when dividing by (x +- p) where p is a constant?

A

Divide the first term by x

Then multiply the new x term by the factor (x +- p)

Subtract that new term from the section above it.

Write the answer of that below

‘drop’ the next term (from the original equation) and put it next to your answer you just got.

Divide the first term of that answer by x

And repeat the steps until you get to the end.

3
Q

What are the 2 things that factor theorem states if f(x) is a polynomial?

A

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.

4
Q

What is proof through deduction?

A

Starting from known facts or definitions, then using logical steps to reach the desired conclusion.

5
Q

When proving something mathematically, what 5 things must you do?

A

You must:

State any information or 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 possibly cases.

Write a statement of proof at the end of your working.

6
Q

What 3 things should you do when proving an identity?

A

You should:

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.

7
Q

What is proof by exhaustion?

A

It means breaking the statement into smaller cases and solving each case separately.

8
Q

What is proof by a counter-example?

A

It is one example that does not work for the statement.

This only needs one example to disprove a statement.