i understand the concepts and all the theorems for this topic, i am able to do some questions, but have difficulty with others, and also factorising cubic equations from scratch. thanks for helping will +reps for everyone, over a period of a few days(:
1. Given that f(x)=x^2n - (p+1)x^2 +p where n and p are positive. Show that (x+1) is a factor of f(x) for all values of p. When p=4, find the value of n for which (x+2) is a factor of f(x) and, for this case, factorise f(x) completely.
2. The expression 2x^3 - 3x^2 +ax +2 leaves a remainder of R when divided by 2x+1 and a remainder of 4R+5 when divided by x-3. Find the value of a.
3. Factorise the expression 6x^3 - 7x^2 - x +2 fully. Hence find all the factors of 6(y+1)^3 - 7(y+1)^2 -y+1,
solve the equation 3(2)^3p+1 + 2 = 7(2)^2p + 2^2p, giving the values of p to two decimal places where necessary.
4. find the value of p for which (2+p)x + 6px^2 + p^2 -4p is divisible by x-1 but not x+1.