Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = x^{2}, \, x = 0$

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

Find the value of the polynomial $p(x) = 5x - 4x^2 + 3$ at $x = 2$.

Evaluate the following product without multiplying directly: $103 \times 107$

Find the zero of the polynomial: $p(x) = cx + d$,where $c \neq 0$ and $c, d$ are real numbers.

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.