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

Verify: $x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$

Without actually calculating the cubes,find the value of each of the following: $(-12)^{3} + (7)^{3} + (5)^{3}$

Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = kx^2 - 3x + k$.

Write the coefficients of $x^2$ in each of the following:
$(i)$ $2+x^2+x$
$(ii)$ $2-x^2+x^3$

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = x^3 - 4x^2 + x + 6$,$g(x) = x - 3$.