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How do I divide this with polynomial division (c4)

I am doing partial fractions which is easy enough but there is this one situation which I cant solve.

Here is the question
6af75de890d49e490bbdc4896e9f0971.png

I understand that it is improper and I have to use polynomial division to split it into a form which I can work with. I understand the concept of this method and I can do questions where you divide x^2 terms but I dont know how you start this off. do I divide 4x by x^2, 6x or something else?

Thanks
Original post by BenGeorge
I am doing partial fractions which is easy enough but there is this one situation which I cant solve.

Here is the question
6af75de890d49e490bbdc4896e9f0971.png

I understand that it is improper and I have to use polynomial division to split it into a form which I can work with. I understand the concept of this method and I can do questions where you divide x^2 terms but I dont know how you start this off. do I divide 4x by x^2, 6x or something else?

Thanks


Actually, I think you'd be okay with just starting with (A/(x+3)) + (B/(x+2)^2) like when you have a repeated linear factor (I think that it's a proper fraction already).

Which is why you're having trouble dividing 4x by x^2, which is what you would start with in long division.
Original post by SeanFM
Actually, I think you'd be okay with just starting with (A/(x+3)) + (B/(x+2)^2) like when you have a repeated linear factor (I think that it's a proper fraction already).

Which is why you're having trouble dividing 4x by x^2, which is what you would start with in long division.


ok it seems i don't know how to identify an improper fraction. I thought it was when the numerator was greater than the denominator. how would I tell that it is proper or improper on an algebraic fraction?
(edited 8 years ago)
Original post by BenGeorge
ok it seems i don't know how to identify an improper fraction. I thought it was when the numerator was greater than the denominator. how would I tell that it is proper or improper on an algebraic fraction?


That;s true, but for fractions with polynomials it's improper if the degree of the numerator is greater than the degree of the denominator.

The degree of a polynomial is the greatest number to which x is raised in that polynomial, so for (1-x) it's 1, (x+7x^2 +5) it's 2, etc.

In this case, what are the degrees of the numerator and the denominator? So is it proper or improper?
Original post by SeanFM
That;s true, but for fractions with polynomials it's improper if the degree of the numerator is greater than the degree of the denominator.

The degree of a polynomial is the greatest number to which x is raised in that polynomial, so for (1-x) it's 1, (x+7x^2 +5) it's 2, etc.

In this case, what are the degrees of the numerator and the denominator? So is it proper or improper?


oh i remember my teacher saying this now. Thanks buddy

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