Given that $q(x)$ has a factor $(x - 4)$, find the value of $k$.

Hence or otherwise, factorize $q(x)$ as a product of linear factors.

$q(4) = 0$     (M1)

$192 - 176 + 4k + 8 = 0{\text{ }}(24 + 4k = 0)$     A1

$k =  - 6$     A1

[3 marks]

$3{x^3} - 11{x^2} - 6x + 8 = (x - 4)(3{x^2} + px - 2)$

equate coefficients of ${x^2}$:     (M1)

$- 12 + p =  - 11$

$p = 1$

$(x - 4)(3{x^2} + x - 2)$     (A1)

$(x - 4)(3x - 2)(x + 1)$     A1

Note:     Allow part (b) marks if any of this work is seen in part (a).

Note:     Allow equivalent methods (eg, synthetic division) for the M marks in each part.

[3 marks]