Use Remainder Theorem to factorise the following polynomials completely :

(i) 2x³ + x² - 13x + 6

(ii) 3x³ + 2x² - 19x + 6

(iii) 2x³ + 3x² - 9x - 10

(iv) x³ + 10x² - 37x + 26

If (2x + 1) is a factor of 6x³ + 5x² + ax - 2, find the value of a.

If (x - 2) is a factor of 2x³ - x² - px - 2, then

(i) Find the value of p.

(ii) with this value of p, factorise the above expression completely.

What number should be subtracted from 2x³ - 5x² + 5x so that the resulting polynomial has 2x - 3 as a factor?