Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(i) p(x) = 2x³ + x² - 2x - 1, g(x) = x + 1

(ii) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

(iii) p(x) = x³ - 4x² + x + 6, g(x) = x - 3

Find the value of k, if x - 1 is a factor of p(x) in each of the following cases:

(i) p(x) = x² + x + k

(ii) p(x) = 2x² + kx + $\sqrt{2}$

(iii) p(x) = kx² - $\sqrt{2}$x + 1

(iv) p(x) = kx² - 3x + k

Factorise :

(i) x³ - 2x² - x + 2

(ii) x³ - 3x² - 9x - 5

(iii) x³ + 13x² + 32x + 20

(iv) 2y³ + y² - 2y - 1

Use suitable identities to find the following products:

(i) (x + 4)(x + 10)

(ii) (x + 8)(x - 10)

(iii) (3x + 4)(3x - 5)

(iv) (y² + $\dfrac{3}{2}$) (y² - $\dfrac{3}{2}$)

(v) (3 - 2x)(3 + 2x)