Maths Questions ^_^

[Odette]

Ok since I seem to have a few questions regarding maths, from now on i'll post them up in this thread.
Here's one i had a bit of trouble with:
1.Given that [x^3 - 3x^2 - 4x +16 = (well its actually 3 -) (x-2) (x+3) (x-c) + Px + Q], Find the values of P, Q and c.
Oh and what does the 3 -s mean?  (Hope that made sense)
Thanks in advance ^_^

Edit: by the 3 -s i mean ≡ Lol

[AppleXY]

Umm. Maybe you should word your question better.

Did you mean (well actually 3 - s) ?

But I don't know where the 3 - s came from, unless if it's a factor.

[Odette]

No i meant ≡ Lol just couldnt find the symbol for it =P

[Odette]

Oh new question...
2.a) Three of the factors of x^4 + ax^3 + bx^2 + x +c are x, x+1 and x-1. Find a,b and c...
   b) Write down an expression of the form x^3 + px^2 + qx + r which gives a remainder 4 when divided by x, x-2 or x+3.

Thanks ^_^

[/0]

Ok since I seem to have a few questions regarding maths, from now on i'll post them up in this thread.
Here's one i had a bit of trouble with:
1.Given that [x^3 - 3x^2 - 4x +16 = (well its actually 3 -) (x-2) (x+3) (x-c) + Px + Q], Find the values of P, Q and c.
Oh and what does the 3 -s mean?  (Hope that made sense)
Thanks in advance ^_^

Edit: by the 3 -s i mean ≡ Lol

The (\equiv) symbol means that the LHS = RHS for all x. It is called an identity. It is unlike an equation in that you can't solve for x.

An easy way is to expand the RHS and group terms:

1





Then you get simultaneous equations:







And you can solve

[Odette]

Oh thank you! ^_^ I get it now lolz + 1 coming your way

[AppleXY]

yeah, means congruent to or "equal", as DB0 said, "identity".

[Odette]

Ok here's one i've started to solve but didnt quite get the answer for...
(1 + tanx ) ^2
I ended up with 1 + 2tanx + tan ^2 x ...
How do you simplify that even further?

[Collin Li]

, since



That's all I can think of.

[Odette]

ahh thanks ! i didnt know 1 + tan ^2 x = sec ^2 x (i'm new to this lolz)

Oh another question i was a little confused about:
 sin ( pi/2 - x) [secx - cosx]

P.S i dont know how to use latex or whatever its called.

[Collin Li]

ahh thanks ! i didnt know 1 + tan ^2 x = sec ^2 x (i'm new to this lolz)

It comes from , and dividing both sides by .

Oh another question i was a little confused about:
 sin ( pi/2 - x) [secx - cosx]

P.S i dont know how to use latex or whatever its called.

You can simplify into . This can be shown geometrically by drawing any right-angled triangle with an angle . The other angle must be , since a triangle has angles adding up to . I've only briefly outlined this, so if you don't get it, ask about it.

This should now yield:

LaTeX is pretty straightforward. Here are some links, give it a go - you learn best by experimenting:
http://vcenotes.com/forum/index.php/topic,864.0.html
http://www.artofproblemsolving.com/LaTeX/AoPS_L_GuideSym.php

[Odette]

Ah does that have anything to do with the sine and cosine graphs being similar except one is moved to the right pi/2 units? (i dunno something the lecturer mentioned today)

And thanks again ^_^ I appreciate it

[Collin Li]

Ah does that have anything to do with the sine and cosine graphs being similar except one is moved to the right pi/2 units? (i dunno something the lecturer mentioned today)

Yeah, that's another way you can think of it. You should try the right-angled triangle method though, it's rather nice.

[Odette]

Ah does that have anything to do with the sine and cosine graphs being similar except one is moved to the right pi/2 units? (i dunno something the lecturer mentioned today)

Yeah, that's another way you can think of it. You should try the right-angled triangle method though, it's rather nice.

Ok, um any link for that one? I've never heard of that method, so i'm not too sure what you're talking about.

[Odette]

Ah never mind i did some research and found out what you were talking about
Thanks again coblin =) it's pretty straight forward now. Oh and i'll practice using LaTeX from now on