CAIE IGCSE Additional Math 3 Factors of Polynomials Topic Practice

The polynomial p is such that $\mathrm{p}(x)=x^{3}+a x^{2}+b x-2, \quad$ where a and b are constants.
It is given that:
- x+2 is a factor of p(x)
- when p(x) is divided by x-3 the remainder is 40.

Find the values of a and b.

DO NOT USE A CALCULATOR IN THIS QUESTION.
Find the x-coordinates of the points of intersection of the curves $y=7x^3-7x^2-17x-4$ and $y=x^3-2x^2-4x-16$.

The polynomial p is such that $\mathrm{p}(x)=a x^{3}+11 x^{2}+b x+c$, where a, b and c are integers. It is given that $\mathrm{p}^{\prime}(0)=12$.
It is also given that x+3 is a factor of p.
When p is divided by x-1 the remainder is 16.
Find the values of a, b and c.