Find the value of the polynomial $x^{2}-7x+12$ at $x=-2$.

With the help of the remainder theorem,examine whether $x+2$ is a factor of the polynomial $x^{3}+9x^{2}+26x+24$ or not.

Write whether the statement is True or False. Justify your answer.
Zero of a polynomial is always $0$.

Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not: $3x^2 + 5x - 7 + \frac{8}{x}$

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x + 6$.

Factorise $x^{3}+8x^{2}+9x-18$.