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# C3 Remainder Theorem watch

1. Using the identity

F(x) ≡ Q(x) x divisor + remainder

How do you know when the remainder is quadratic or linear?

Im doing myself so i need a bit of help.
2. It depends on what order polynomial you start with, and what you're dividing by.
I've never seen this being asked though in an exam don't quote me though.
3. i still dont understand why the remainder is an interger in this case. Can someone explain when to use a linear remainder or an interger or a quadratic remainder...!!
4. Well if you were to do algebraic division, you can see this.
I've just tried a couple of examples to see. I remember thinking exactly the same some time back, so i figured out that if you take the numerators index away from the denominators ie. 4-2. you know that it's going to be a binomial. ie x^2 is going to be the Q(x) therefore you must allow yourself Ax+B at least. then the remainder, you need to look at the eq again, and in x^4+1, you see that 1 is not divisible by x^2. so it's an integer remainder so only add D

If however, it was x^4+x^2+x./x^2 then do the same procedure 4-2. so (Ax^2+Bx+C)(x^2) + Dx+E as you can see x is not divisible by x^2.

Even though some letters equal 0, that's not a problem. it's correct. check by division.
hope that clears it up a bit for you.
5. Hmm....thanks for that little help there....Ill do some examples and see if this works.

Thanks again.
6. (Original post by Bengaltiger)
Using the identity

F(x) ≡ Q(x) x divisor + remainder

How do you know when the remainder is quadratic or linear?

Im doing myself so i need a bit of help.
In general the degree of the remainder will be strictly less than that of the divisor.

So if you divide by a quadratic the remainder will be at most degree one; it may also be a constant or even zero if the quadratic divides exactly

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