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Given the polynomial P(x) = 2x³ - x² + ax + b - 12.

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1. i) (a) Find the values of the constants aa and bb.
Given the polynomial P(x)=2x3−x2+ax+b−12P(x) = 2x^3 - x^2 + ax + b - 12.

Step 1: Use the Remainder Theorem.
When P(x)P(x) is divided by (x+3)(x+3), the remainder is 18. This means P(−3)=18P(-3) = 18.

P(−3)=2(−3)3−(−3)2+a(−3)+b−12=18P(-3) = 2(-3)^3 - (-3)^2 + a(-3) + b - 12 = 18
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