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C3 Solomon Paper Question

I am doing Solomon Paper A and am stuck on 7.a)i)
Show that
sin (x + 30)° + sin (x − 30)° ≡ a sin x°,
where a is a constant to be found.
I have managed to get to 2sinxcos30 but I don't know where to go from here, looking at the mark scheme hasn't helped, all I know is that it should end up as root 3 sin x

Reply 1

penta

cos 30 = (root 3)/2
Therefore when multiplied by two it equals just root three = a

Reply 2

PF37

Thank you, another question I need to do a polynomial division of (x^4+x^3-5x^2-9)/(x^2+x-6) I ultimately need to do a partial fraction but first I need to divide and I am stumped

Reply 3

PF37

Thank you, another question I need to do a polynomial division of (x^4+x^3-5x^2-9)/(x^2+x-6) I ultimately need to do a partial fraction but first I need to divide and I am stumped

Reply 4

davros

Original post by PF37

Thank you, another question I need to do a polynomial division of (x^4+x^3-5x^2-9)/(x^2+x-6) I ultimately need to do a partial fraction but first I need to divide and I am stumped

Just imagine you're doing a normal numeric long division and start with the basics.

How many "times" does x^2 go into x^4?

Reply 5

TenOfThem

Original post by PF37

Thank you, another question I need to do a polynomial division of (x^4+x^3-5x^2-9)/(x^2+x-6) I ultimately need to do a partial fraction but first I need to divide and I am stumped

You do not need to divide at all

\dfrac{x^4+x^3-5x^2-9}{x^2+x-6} = x^2 + Ax + B + \dfrac{C}{x+3} + \dfrac{D}{x-2}

You just do partial fractions

(edited 9 years ago)

Reply 6

PF37

Could you explain it step by step please

Reply 7

TenOfThem

Original post by PF37

Could you explain it step by step please

I assume (given you did not use the quote facility) that you are talking to me

What do you want me to explain

Reply 8

PF37

anyone really, the question is f(x) = (x^4+x^3-5x^2-9)/(x^2+x-6)
.
(a) Using algebraic division, show that
f(x) = x^2 + A + B/(x+c),
where A, B and C are integers to be found.
I really struggle when you have to do polynomial division with anything more that x^2 + c

Reply 9

TenOfThem

Original post by PF37

I really struggle when you have to do polynomial division with anything more that x^2 + c

You really need to ask a teacher that can sit with you - this is a topic that needs step by step discussion and cannot easily be explained on a forum

There are some exam solutions and youtube videos that you could watch

Reply 10

davros

Original post by PF37

You haven't shown us any attempted working yet!

As I asked earlier, how many "times" does x^2 go into x^4?

Reply 11

PF37

Original post by davros

As I asked earlier, how many "times" does x^2 go into x^4?

x^2 times, i can do the simple ones just not these complex ones

Reply 12

davros

Original post by PF37

x^2 times, i can do the simple ones just not these complex ones

Same principle!

You can write down x^2 straight away, then multiply x^2 into x^2 + x - 6, subtract the result from the original quartic polynomial and write down the next partial result in the process.