Further Mathematics Past Questions and Answers

If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p

For what value of k is 4x\(^2\) - 12x + k, a perfect square?

A binary operation * is defined on the set of real numbers, R, by
P * q = \(\frac{q^2 - p^2}{2pq}\). Find 3 * 2

Find the inverse of \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)

Given that P = { x: 0 ≤ x ≤ 36, x is a factor of 36 divisible by 3} and Q = { x: 0 ≤ x ≤ 36, x is an even number and a perfect square}, find P n Q.