I'm stuck with quite a few questions:
4. Given that x[^2] + 1 is a factor of px[^3] + qx[^2] + px + q, find the other factor.
8. Construct a cubic equation with roots -









10. f(x) = 5x[^3] - x[^2] - 1
a) Find the remainder when f(x) is divided by 2x - 1.
I got remainder -0.625.
b) Write f(x) in the form (2x - 1)Q(x) + R where Q(x) is a quadratic expression and R is a constant.
c) Write f(x) in the form k[(2x - 1)(ax[^2] + bx + c) + d] where a, b, c and d are integers and k is rational.
12. f(x) = 4x[^3] + 4x[^2] - 21x + 9
a) Find the remainder when f(x) is divided by x - 1.
I got remainder -4.
b) The coefficient of x in f(x) can be altered so that when the new f(x) is divided by x - 1 the remainder is zero. Find the new coefficient.
Any help would be much appreciated,
Thanks.