Rationalize the denominator and simplify: \( \frac{2+\sqrt{6}}{\sqrt{3}} \)

Factorise the following polynomial express theorem: \( f(x)=x^{3}-2 x^{2}-5 x+6 \)

Given a singular matrix \( B=\left[\begin{array}{cc}\lambda-4 & 4 \\ 5 & \lambda-3\end{array}\right] \begin{array}{l}\lambda \text { determine the values of } \lambda . \\ \lambda=1 \text { or }-8 .\end{array} \)

Mathematics/P1 QUESTION 1 \( \begin{array}{ll}1.1 & \text { Solve for } x \text { - Grade } 11 \\ 1.1 .1 & x^{2}+5 x-6=0 \\ 1.1 .2 & 5 x^{2}+2 x-6=0 \text { (correct to TWO) decimal places) } \\ 1.1 .3 & (2 x+3)(3-x)>4 \\ 1.1 .4 & \sqrt{x+2}+x=4\end{array} \)

Factorise the following as far as possible in \( \left(3 x^{2}+7 x\right)^{2}-4\left(3 x^{2}+7 x\right)-12 \)

Write the following expressions as simply as possible in correct algebraic notation: a) \( 7 d \times 5 \) (b) \( 12 r \div 4 \)