methods3/4 q's

[Nato]

does the remainder theorem work when diving some polynomial by a quadratic?

such as trying to find the remainder when (from essentials textbook) is divided by . Can this be done without having to do the whole long division?

cheers.

[Orb]

does the remainder theorem work when diving some polynomial by a quadratic?

such as trying to find the remainder when (from essentials textbook) is divided by . Can this be done without having to do the whole long division?

cheers.

There's a thread for 3/4 MM questions btw.

But anyway, I don't believe that the remainder theorem can be used to apply in this circumstance. You can't simply sub in x=1 to find the solution because x^2 is made out of (x+1)(x-1).

So yeah, you should just divide the polynomial through the long division method.

[psyxwar]

After looking through my essentials, I found the question:

Given that P(x) can be written in the form , where Q(x) is a polynomial and a and b are constants, hence or otherwise, find the remainder when P(x) is divided by





Adding the two equations we get: , from which we get and

Therefore, the remainder, which is ax+b, is 6x-4.

[Nato]

this is from essentials.

Well, the graph of is shown. Then we are told to graph (question a) ->  by 'applying suitable transformations'. I don't think we're supposed to expand it or anything.

I am finding it hard to see the transformations that have taken place. Can anyone provide any hints? Like, could the equation be arranged a certain way?

thanks

[Phy124]

If and then they are related by i.e. the graph of is obtained by translating one unit to the right.