How to find algebraic values of a and b in polynomial function using a zero and a factor plus it's rest?

Question

Consider the following equation:

$P(x)=ax^3+3x^2+bx+3$

P(x) contains one zero at x = 1. When P(x) is divided by (x-2), the rest is 15.

How can I find the values of a and b, and how might I find the solution to the inequation P(x)≤ 0?

Answer 1

"$P(x)$ contains one zero at $x = 1$. When $P(x)$ is divided by $(x-2)$, the rest is $15$."

This means that $P(1)=0$ and $P(2) = 15$. These two equations give to you a linear system on $a$ and $b$. Can you follow from here?