Express $\frac{4}{( x - 1 ) ( x + 3 )}$ in partial fractions.

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The cubic $f (x) = 2 x^{3} - 3 x^{2} - 11 x + 6$ has $(x - 3)$ as a factor. What are all its roots?
The function $f (x) = \frac{2 x + 1}{x - 3}$ is defined for $x \neq = 3$ . What is $f^{- 1} (x)$ ?
Complete the square for $2 x^{2} - 12 x + 5$ . Which expression is equal to it?
The roots of $2 x^{2} - 7 x + 3 = 0$ are $α$ and $β$ . What is the value of $α^{2} + β^{2}$ ?
Solve $x^{2} - 5 x - 14 > 0$ .
When $x^{3} + k x^{2} - 4 x + 12$ is divided by $(x + 2)$ the remainder is $4$ . What is $k$ ?