Find p(0), p(1) and p(2) for each of the following polynomials:

(i) p(y) = y² - y + 1

(ii) p(t) = 2 + t + 2t² - t³

(iii) p(x) = x³

(iv) p(x) = (x - 1) (x + 1)

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) p(x) = 3x + 1, x = $-\dfrac{1}{3}$

(ii) p(x) = 5x - π, x = $\dfrac{4}{5}$

(iii) p(x) = x² - 1, x = 1, -1

(iv) p(x) = (x + 1)(x - 2), x = -1, 2

(v) p(x) = x², x = 0

(vi) p(x) = lx + m, x = $-\dfrac{m}{l}$

(vii) p(x) = 3x² - 1, x = $-\Big(\dfrac{1}{\sqrt{3}}\Big)$, $\Big(\dfrac{2}{\sqrt{3}}\Big)$

(viii) p(x) = 2x + 1, x = $\dfrac{1}{2}$

Determine which of the following polynomials has (x + 1) a factor :

(i) x³ + x² + x + 1

(ii) x⁴ + x³ + x² + x + 1

(iii) x⁴ + 3x³ + 3x² + x + 1

(iv) x³ - x² - (2 + $\sqrt{2}$)x + $\sqrt{2}$

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