Find in each case, the remainder when :

x³ + 3x² - 12x + 4 is divided by x - 2.

Find in each case, the remainder when :

x⁴ + 1 is divisible by x + 1.

Use the Remainder theorem to find which of the following is a factor of 2x³ + 3x² - 5x - 6.

(i) x + 1

(ii) 2x - 1

(iii) x + 2

If 2x + 1 is a factor of 2x² + ax - 3, find the value of a.