Project Maths Algebra, please help

ampmm

So I'm in 5th year now, doing algebra (chapter 3 in Active Maths 4 Book 1) and am totally lost.. I was always a good maths student but I've completely slipped on this chapter.. I have no idea how to even begin questions or what I'm looking for (3.8 in particular)..





x2-ax+2 is a factor of x3-x2+5ax-b
Express a in terms of b







If any can help explain this one (it's q21 on page62) I'd really really apreciate as I am completely at a loss...


Thanks in advance

CookieMonster.x

ampmm wrote: »

So I'm in 5th year now, doing algebra (chapter 3 in Active Maths 4 Book 1) and am totally lost.. I was always a good maths student but I've completely slipped on this chapter.. I have no idea how to even begin questions or what I'm looking for (3.8 in particular)..





x2-ax+2 is a factor of x3-x2+5ax-b
Express a in terms of b







If any can help explain this one (it's q21 on page62) I'd really really apreciate as I am completely at a loss...


Thanks in advance

Since it's a factor it will divide in with no remainder. So you just divide x3-x2+5ax-b by x2-ax+2. It's a little tricky to get used to but it's the exact same as normal division. When you get to the last 2 lines, you know that they are equal so you let them equal each other. One will have a and b in it so you just move the b terms to one side to get a.
I think the last 2 lines are
(5a-2)x - b
(-a-a2)x + 2 + 2a.
Let 5a-2=-a-a2 and -b=2+2a.
I think I've a wrong sign somewhere though.
I probably haven't explained that properly, it took me a few questions to get the hang of it. If you want more help just ask

whiteandlight

Are you confident with standard long division/finding factors? That's what's needed here

ampmm

I've gotten some numbers and letters but I don't know what any of them represent

whiteandlight

Ok can you have a watch of this and see if you understand it and we'll work from there.

http://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/algebraic-long-division

poggy

The first thing you need to do is make sure ya know what you are looking for and what operations will give you what you want with what you have.

Here you have a factor of a polynomial there for long division will give you a remaining factor.

here is and example of long division http://www.sosmath.com/algebra/factor/fac01/fac01.html

the remaining factor should be in terms of a and b.

Hope this helps.

whiteandlight

poggy wrote: »

The first thing you need to do is make sure ya know what you are looking for and what operations will give you what you want with what you have.

Here you have a factor of a polynomial there for long division will give you a remaining factor.

here is and example of long division http://www.sosmath.com/algebra/factor/fac01/fac01.html

the remaining factor should be in terms of a and b.

Hope this helps.

I like that link

ampmm

Thanks for all your help guys,







I tried to do the long division way there and now after getting as far as dividing x+(a-1) I've got (and after changing the signs)

+x(5a-2)-b
+ax(a-1) -2(a-1)




Am I completely wrong or does anyone know where I wemt wrong?


I wish I could just send a pic of my work, would make life so much easier

whiteandlight

May have made a mistake but you are nearly there well done. Here's mine-not sure if its fully correct as I'm rushing away now.

CookieMonster.x

ampmm wrote: »

Thanks for all your help guys,







I tried to do the long division way there and now after getting as far as dividing x+(a-1) I've got (and after changing the signs)

+x(5a-2)-b
+ax(a-1) -2(a-1)

Am I completely wrong or does anyone know where I wemt wrong?

I wish I could just send a pic of my work, would make life so much easier

The answer at the back is a=1 - 1/2b which is what I got apart from the wrong sign. You have the answer (only the sign is wrong according to the answer at the back).
You let
-b = -2(a-1) and work out the brackets. You only need to do this one because you're only asked to express a in terms of b.
So -b=-2a+2,
2a = 2 + b
A = 2+b/2(all over 2) which is the same as 1 + b/2.