Cubic equations and their factorization

Weekend Assignment

Given that a cubic equation x³ + 2x² – 19x – 20 = 0 has 4 as one its roots, find the

(1) Second root                        (a) -1               (b) 1                (c) 2                 (d) 3

(2) Third root                           (a) 5                 (b) -8               (c) 3                 (d) 2
(3) Sum of the second and third roots (a) -4       (b) 6                   (c) 4         (d) -6

(4) Product of the second and third roots             (a) 6      (b) 5       (c) -6      (d) -5

(5) Find the zeros of x² – 1                  (a) 2 or -2     (b) 1 or 2    (c) -1 or 1     (d) 1 or -2

Theory

(1) If (x + 1) is a factor of f(x) = x³ + kx² + 3x + 10, find the value of the constant k.

(2) Factorise f(x) completely.