Find the zero of the polynomial: $p(x) = 3x$

Check whether $7+3x$ is a factor of $3x^3+7x$.

Expand each of the following,using suitable identities: $(2x - y + z)^2$

Factorise: $27x^3 + y^3 + z^3 - 9xyz$

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $5+2x$.

Verify whether the following are zeroes of the polynomial indicated against them:
$p(x) = 3x^2 - 1, x = -\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$