Given the polynomial P(x) = 2x^3 - x^2 + ax + b - 12.
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
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1. i) (a) Find the values of the constants $a$ and $b$.
Given the polynomial $P(x) = 2x^3 - x^2 + ax + b - 12$.
Step 1: Use the Remainder Theorem.
When $P(x)$ is divided by $(x+3)$, the remainder is 18. This means $P(-3) = 18$.
$$P(-3) = 2(-3)^3 - (-3)^2 + a(-3) + b - 12 = 18$$
$$2(-27) - 9 - 3a + b - 12 = 18
