Expand

$\left(\frac{2 x}{3}+\frac{4 y}{5}\right)\left(\frac{2 x}{3}-\frac{4 y}{5}\right)$

From the following polynomials find out which of them has $(x+1)$ as a factor

$x^{3}+10 x^{2}+23 x+14$

Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not

$x^{3}+y^{3}+z^{3}-3 x y z$

Factorise $x^{2}-7 x+12$ by using the factor theorem.

By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where

$p(x)=x^{3}-6 x^{2}+2 x-4, \quad g(x)=1-\frac{3}{2} x$

Verify whether the following are True or False:

$-3$ is a zero of $y^{2}+y-6.$