Im stuck on the following questions and need some help. Sorry I dont know how to do X squared on the keyboard so X^2 means X squared and etc.

1. Simplify 4X^5 + 16X / 4X

b. Simplify 2X^2 +11X +12 / 2X^2 + X-3

2. Divide X^3 - 5X^2 + X + 10 by X-2

b. Divide X^3 - 27 by X-3

3. (X-2) is a factor of f(X) = X^3 + 7X^2 + qX - 40 therefore find q

4. Show that (2X-1) is a factor of 2X^3 + X^2 + X-1 and then find the quadratic factor.

5. f(X) = X^3 + pX^2 -49X -120 given that f(-5) = 0, find p

b. Factorise f(X) completely into linear factors

6. A function is given as f(X) = aX^3 + bX^2 + X-10. When f(X) is divided by (X-2) the remainder is 36. (X+2) is a factor of f(X), show that a=2 and then find the value for b.

7. A function is given as f(X) = X^3 + aX^2 + bX + 6. Find in terms of a and b, the remainder when f(X) is divided by

a. (X-2)

b. (X+3)

then given that these remainders are equal express a in terms of b.

8. Find the remainder when 2X^2 + 4X - 5 is divided by (2X+1)

Sorry I asked for so much, these are past paper questions that I don't understand, so sorry to cause trouble and if you dont mind can you also write out your workings as well to see how to come to that conclusion so I can handle questions of the smilar sort as future reference.

This needs to be in by tomorrow so its in a hurry.

Thank You.