Factorise
$\frac{4 x^{2}}{9}-\frac{x}{3}+\frac{1}{16}$
$\left(\frac{2}{3} x-\frac{1}{4}\right)^{2}$
Write whether the following statements are True or False. Justify your answer.
$\frac{6 \sqrt{x}+x^{\frac{3}{2}}}{\sqrt{x}}$ is a polynomial, $x \neq 0$
On dividing $p(x)=x^{3}+2 x^{2}-5 a x-7$ by $(x+1),$ the remainder is $R _{1}$ and on dividing $q(x)=x^{3}+a x^{2}-12 x+6$ by $(x-2), \quad$ the remainder is $R _{2} .$ If $2 R _{1}+ R _{2}=6,$ then find the value of $a$.
$x^{2}+\frac{y^{2}}{4}+\frac{z^{2}}{16}+x y+\frac{y z}{4}+\frac{z x}{2}$
State whether each of the following statements is true or false
$x^{2}-8 x+12=(x-6)(x-2)$
Find the value of the polynomial $3 x^{3}-4 x^{2}+7 x-5,$ when $x=-3$
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