Determine whether $(x+1)$ is a factor of the polynomial $p(x) = x^{3} - 2x^{2} - 5x + 6$.

Factorise the following quadratic polynomial by splitting the middle term:
$6x^2 + 19x + 10$

Verify whether $3$ and $7$ are zeros of the polynomial $p(x) = x^{2} - 5x - 14$ or not.

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: $x^{2}-8x+15$

If both $x-2$ and $x-\frac{1}{2}$ are factors of $p x^{2}+5 x+r,$ show that $p=r$.

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