1. The function f(x) = 2x^3 +ax^2 -bx +3 has a factor (x+3). When f(x) is divided by (x-2), the remainder is 15.
a. Calculate the values of a and b
b. Find the other two factors of f(x)
2. Let P(x)=x^5-3x^4+2x^3-2x^2+3x+1
Given that P(x) can be written in the form (x^2-1)Q(x)+ax +b where Q(x) is a polynomial and a and b are constants, hence or otherwise, find the remainder when P(x) is divided by x^2-1
3. The expressions px^4-5x+q and x^4-2x^3-px^2-qx-8 have a common factor x-2. Find the values of p and q
4. Write down one quadratic factor of x^4+x^3-x^2-3x-6, and find a second quadratic factor.
ps theses are questions from my textbook so i know wot the answers r i just can't get to them. if u don't might could u explain what ur doing.thanks.