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# Algebraic Long-Division, where the divifing \$x\$ has a co-efficient

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1. I know how to do algebraic long division when dividing by (X+a) however when a co-efficient is added to the X what do you do? e.g (x^{3}-4x^{2}+12)/(3x-4) I recall you having to times by the co-efficient and then dividing by a - or something like so.

I resulted to dividing both the top and bottom of the fraction by the co-efficient to rid X of its co-efficient, and then long-divide traditionally, but this seems like an over-complication and makes lots of room for error as an abundance of fractions are created.
2. If you don't change the 3x-4 to 3(x-4/3) and taking out the 1/3 you will end up with a load of fraction in the answer anyway. In other words without taking the 3 out, you first element in the answer would be (x^2)/3.

I am not sure if this answers your question.
3. to divide f(x) by (3x - 4)...

you do the usual sequence of steps... divide, multiply, subtract, bring down terms... but the dividing is by 3x instead of just x.

so you begin...

x3 divided by 3x is x2 /3

then multiply 3x -4 by x2 /3

etc
4. (Original post by the bear)
to divide f(x) by (3x - 4)...
x3 divided by 3x is x2 /3

then multiply 3x -4 by x2 /3

etc
So in this case you will end up with a deal of fractions to manage, either way.

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