Multiple unknown constants

Given one factor of a polynomial with two or more unknown constants, express one constant in terms of another or find relationships between them using the factor theorem.

1 questions

CAIE P2 2019 June Q1

1 The polynomial $\mathrm { p } ( x )$ is defined by $$\mathrm { p } ( x ) = 4 x ^ { 3 } + ( k + 1 ) x ^ { 2 } - m x + 3 k$$ where $k$ and $m$ are constants. Given that $( x + 1 )$ is a factor of $\mathrm { p } ( x )$, express $m$ in terms of $k$.