Families of functions question

[xce]

Hi all,

We have been given an assignment on Chapter 3: Families of functions (Essential Math Methods 3&4 textbook). I have been able to answer all questions on the assignment easily (the assignment is quite easy), apart from one of them. Any help is appreciated.

Express in the form

Thanks!

[bucket]

i know this one!..i think?

editsorry, it turns out i only know how to work it out without the coefficients too =\ lol. how embarrasing







thats as far as I can go =\ sorry.

[xce]

Heard of the question? It's from the assignment they ship on the Teacher's CD-ROM. I'd imagine quite a few schools use it.

I should also add that the textbook gives an example on how to do it, but only for questions where there is no coefficient in front of the x term. Therefore, the example was unhelpful.

[AppleXY]

--> Disregard. Miscalc.

[bucket]

apple are you sure that is right? because when I put your equation into the calculator with x=2, it doesn't get the same answer as the original equation.

[AppleXY]

Disregard. Something went terribly wrong. Sorry, I have to check over it again, but now I gotta do my Identity & Belonging crap for english.

[dcc]

I'd do it using long division, as such:

           



       

Remainder:

Thus remembering our form for dividing:

[AppleXY]

lol, bloody hell why use my "alegbraic equality way". Urgh, it was an alternative.

Synthetic Division is always a winnar in these sort of questions.

EDIT: Found way. I'll type the alternative way soon. I SHOULD GET MY ENGLISH DONE

[Toothpaste]

=
times through by 5x+3



To find A eliminate B:
let x =



 


now for B:


let x = 1
... (1)

let x = 0

rearrange
...(2)

sub (2) into (1):






=
put A and B back

=






... same as dcc's ... with partial fractions

[humph]

Hi all,

We have been given an assignment on Chapter 3: Families of functions (Essential Math Methods 3&4 textbook). I have been able to answer all questions on the assignment easily (the assignment is quite easy), apart from one of them. Any help is appreciated.

Express in the form

Thanks!

wow, i'd just do that kinda in my head...



i always just find it easier to manipulate the top line to match the bottom than to do long division or anything like that...

[lanvins]

for the way dcc did it, how did u get q(X) r(x)?

[dcc]

q(x) is like the quotient,  if you divide 12 by 4, 3 is the quotient.
r(x) is the remainder

[AppleXY]

Mmm. In synthetic division (aka Long Div) if you divide q(x) with r(x) this results in partial fractions if the remainder is not 0 [if zero, this will be a  factor of q(x) ].

oh btw, when you obtain a remainder r(x) will be on the denominator.

i.e. + where Y is the constant.

[Mao]

let me have a crack at solving it without long division:

in the form

therefore:





cross multiplying:







therefore:

[1]: , [2]: , [3]:

from [1]: ,

substituting into [2]:







and hence, substituting a and c gives:



yay i got the same as everyone else



..

[AppleXY]

lol, theres many ways to do. But I'd do the synthetic or equalities using >1 coffecients (toothpick's posts).