For the polynomial $p(x),$ if $p(7)=0,$ then .......... is a factor of $p(x)$.

Factorise $x^{3}-11 x^{2}+20 x+32$.

Evaluate the following product without multiplying directly: $103 \times 105$.

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

Check whether the polynomial $p(x) = x^{3} + 9x^{2} + 26x + 24$ is a multiple of $x + 2$ or not.

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = 4x^3 - 12x^2 + 14x - 3$ and $g(x) = 2x - 1$.