How did you secure A* in maths and FM without being able to carry out polynomial division? Your answer is wrong by the way.

mssmith was showing you a shortcut:

\displaystyle \frac{x^3}{1+x^2}=\frac{x(1+x^2)-x}{1+x^2}=x-\frac{x}{1+x^2}

Reply 6

Mr M

Study Forum Helper

Original post by Matthew Campbell

Try substituting in values, that might help.

I know you are only trying to help but please stick to questions where you know what you are doing.

Reply 7

Moordland

Original post by Mr M

How did you secure A* in maths and FM without being able to carry out polynomial division? Your answer is wrong by the way.

mssmith was showing you a shortcut:

\displaystyle \frac{x^3}{1+x^2}=\frac{x(1+x^2)-x}{1+x^2}=x-\frac{x}{1+x^2}

This was only touched upon in C3 when doing a proof, working out constants etc.

And C2 is easy.

Thanks I see what he meant.

(edited 8 years ago)

Reply 8

Mr M

Study Forum Helper

Original post by Moordland

Thanks I see what he meant.

Spoiler

He was trying to give you a clue without giving you the full answer. That's how we try to do things around here.

Reply 9

Moordland

Original post by msmith2512

If you were to write x^3 as (x + x^3 - x) would that help?

Thank you for your reply :smile:

Original post by Mr M

He was trying to give you a clue without giving you the full answer. That's how we try to do things around here.

I agree, that is the best approach to have, since if someone did it forme I woldnt really be learning anything.

Thank you both.

Reply 10

ludmila

Original post by Moordland

Thank you for your reply :smile:

I agree, that is the best approach to have, since if someone did it forme I woldnt really be learning anything.

Thank you both.

OR, whenever you're stuck and can't 'see' what to add, subtract etc., just do the long division; it will give you the same result.

Reply 11

Moordland

Original post by ludmila

OR, whenever you're stuck and can't 'see' what to add, subtract etc., just do the long division; it will give you the same result.

Thanks for the reply, sadly I am stuck :/

Maybe because the division is unconvential I get that it is x^3 but this does not look right :/

Reply 12

davros

Original post by Moordland

Thanks for the reply, sadly I am stuck :/

Maybe because the division is unconvential I get that it is x^3 but this does not look right :/

There's nothing "unconventional" about it - this is standard AS level polynomial division. (That's not to say that this is the only way of going about it, because some people prefer the method that involves writing the numerator as 2 terms - a factor multiplying the denominator plus some unknown polynomial - and then equating coefficients, but you should be at least familiar with the 'basic' method.)

If you had to divide something like

x^3 + x + 1

x^2 + 1

, would you be able to do it? It's exactly the same principle :smile:

Reply 13

DFranklin

Original post by Moordland

Maybe because the division is unconvential I get that it is x^3 but this does not look right :/

As davros says, this is as standard as it gets.

I see you are looking at STEP (and I'm guessing this fraction is from the advpcm.pdf document). For STEP, you need to be thoroughly comfortable with all the material and operations you cover in the Maths A-level. It's not just "you need to be able to do this", it's "you need to be able to be able to glance at this and know you can do it and roughly what form the answer will take". (Being able to get the correct answer in a glance is not essential, but you need to have an idea what it will look like so you have an idea whether dividing out is a sensible thing to do).

To be honest, looking at your recent posts, I think you need to thoroughly revise the A-level syllabus before you take a serious look at STEP.