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

Find the values of constants a and b when x - 2 and x + 3 both are the factors of expression x³ + ax² + bx - 12.

Find the value of k, if 2x + 1 is a factor of (3k + 2)x³ + (k - 1).