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 $a$.

Evaluate the following products without multiplying directly

$78 \times 84$

The following expressions are polynomials? Justify your answer:

$\frac{1}{7} a^{3}-\frac{2}{\sqrt{3}} a^{2}+4 a-7$

Which of the following expressions is a polynomial, state the reason ? If an expression is polynomial, state whether it is a polynomial in one variable or not

$x^{2}+y^{2}+z^{2}+2 x y+2 y z+2 z x$

Classify the following as linear, quadratic or cubic polynomial

$x^{2}-9 x+14$