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# C3 Algebraic Fractions watch

1. Hi, i am going through the C3 maths book, and i came across this:

The remainder theorem: Any polynomial F(x) can be put in the form;

F(x) = Q(x) x divisor + remainder

What does this actually mean?

Thanks!!
2. You can divide a polynomial P by another polynomial Q. If the degree of P is greater than that of Q, the result is a polynomial plus a fraction R/Q where R is a polynomial whose degree is less than that of Q.
3. (Original post by shawn_o1)
You can divide a polynomial P by another polynomial Q. If the degree of P is greater than that of Q, the result is a polynomial plus a fraction R/Q where R is a polynomial whose degree is less than that of Q.

Does this mean that, in an ideal question,i would have to divide a polynomial by long division first to find the remainder. After this, i would use this equation to write it in the form of a mixed fraction?
4. (Original post by JamesNeedHelp2)

Does this mean that, in an ideal question,i would have to divide a polynomial by long division first to find the remainder. After this, i would use this equation to write it in the form of a mixed fraction?
yes
5. (Original post by shawn_o1)
yes
Appreciated!!
6. You don't have to use long division - there are other approaches.
7. (Original post by Muttley79)
You don't have to use long division - there are other approaches.
The remainder theorem? Any other method? Thanks!
8. They will give you a fact ie f(x) has remainder 24 when divided by (x - 2).

So you can write f(x) = (x-2)(polynomial of degree one less than f with unknown coeffs) + 24

Then you compare co-efficients; my students sometimes find this easier than dividing.
9. (Original post by Muttley79)
They will give you a fact ie f(x) has remainder 24 when divided by (x - 2).

So you can write f(x) = (x-2)(polynomial of degree one less than f with unknown coeffs) + 24

Then you compare co-efficients; my students sometimes find this easier than dividing.
Thank you Miss!

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