Given f(x) = 2x^3 + ax^2 - 3x + 1 and the divisor is (x+1), so c = -1.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve Question 1.
The remainder theorem states that if a polynomial $f(x)$ is divided by $(x-c)$, the remainder is $f(c)$.
Given $f(x) = 2x^3 + ax^2 - 3x + 1$ and the divisor is $(x+1)$, so $c = -1$.
The remainder is given as $-2$.
Therefore, $f(-1) = -2$.
Substitute $x=-1$ into $f(x)$:
$$f(-1) = 2(-1)^3 + a(-1)^2 - 3(-1) + 1$$
$$f(-1) = 2(-1) + a(1) +
