2) Factorise the following a) \( x^{2}+x \) b) \( t^{2}-t \) c) \( x^{3}+x \) d) \( x^{5}-x^{2} \) e) \( a^{7}+a^{4} \)

The function \( f(x)=2 x^{2}-5 x+2 k-1 \) does not intersect the \( x- \) axis. Find the range of values of \( k \)

Solve the system of quadratic inequalities: \[ \begin{array}{c}\mathrm{y}>\mathrm{x}^{2}-1 \\ \mathrm{y} \leq-\frac{1}{3} \mathrm{x}^{2}+5\end{array} \]

The ratio of Ben's age to Ali's age is \( 3=2 \). Their total age is 140 years now What is Alils age?

Which expression is equivalent to \(( x^ { \frac { 3} { 7} } ) ^ { 2} \) ?A. \(x^ { \frac { 6} { 14} } \)B. \(x^ { \frac { 17} { 7} } \)C. \(x^ { \frac { 6} { 7} } \)D. \(x^ { \frac { 5} { 7} } \)

Find the points of intersection for the system \[ \begin{array}{l}\mathrm{y} \geq 2 \mathrm{x}^{2}+3 \mathrm{x}-20 \\ \mathrm{y} \leq \mathrm{x}^{2}+\mathrm{x}-5\end{array} \]