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

$5 x^{2}+11 x-2 \sqrt{x}$

By using the factor theorem, show that $(x-3)$ is a factor of the polynomial $12 x^{3}-31 x^{2}-18 x+9$ and then factorise $12 x^{3}-31 x^{2}-18 x+9$

Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by

$x+3$

Classify the following as a constant, linear,quadratic and cubic polynomials:

$4-5 y^{2}$

Factorise

$16 x^{2}+40 x y+25 y^{2}$

Expand

$(2 x-7)(2 x-5)$