bandaid-bandet said:

Determine the remainder when (3x^5-5x^2+4x+1) is divided by (x-1)(x+2).

I'm not sure how you're supposed to use the Remainder Theorem for this...? I would divide by x - 1 and then x + 2 (or the other way 'round), or else divide by their product, x<sup>2</sup> + x - 2.

bandaid-bandet said:

When x+2 is divided by f(x), the remainder is 3. Determine the remainder when x+2 is divided into each of the following:

a) f(x) + 1

Because of the remainder, you have, for some (unspecified) polynomial "p(x)":

. . . . .f(x) = (x + 2)[p(x)] + 3

(This is like when you divide 13 by 4: you get 3, with a remainder of 1. This means that 13 = (3)[4] + 1. I'm doing the same thing in the indented bit above.)

So what happens when you add "1" to both sides? What is the remainder?

bandaid-bandet said:

Do the same sort of thing:

. . . . .f(x) = (x + 2)[p(x)] + 3

. . . . .2f(x) = 2[(x + 2)[p(x)] + 3]

. . . . . . . .. .= (x + 2)[2p(x)] + ??

What's the remainder now?

They should all work similarly. If you're stuck or not sure, please reply showing what you've done. Thank you.

Eliz.