If $x+1$ is a factor of $ax^3+x^2-2x+4a-9$,find the value of $a$.

Factorise $4 x^{2}+9 y^{2}+49 z^{2}-12 x y+42 y z-28 z x$.

Expand $(x+3)(x+8)$.

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: $x^{2}+y^{2}+z^{2}+2xy+2yz+2zx$

Find $p(1)$,$p(2)$,and $p(4)$ for the following polynomial: $p(t) = t^{2} - 6t + 8$.

Check whether $(x-1)$ is a factor of the polynomial $p(x) = x^{3}-7x^{2}+14x-8$.