Use factor theorem to determine whether $g\left(x\right)=2x-3$ is a factor of $p\left(x\right)=x+2x^3-4x^2+12$ or not.

Verify that $\left(x-1\right), \left(x-2\right)$ and $\left(2x+1\right)$ are factors of the polynomial $2x^3-5x^2+x+2$.

Find the value of $k$, if $\left(x-1\right)$ is a factor of $p\left(x\right)=k{x}^2-5x+k$.

Find the value of $k$, if $\left(x-1\right)$ is a factor of $p\left(x\right)=k{x}^2-\sqrt{2}x+3$.

Find the value of $k$, if $\left(x-1\right)$ is a factor of $p\left(x\right)=3x^2+kx+\sqrt{2}$.

Find the value of $k$, if $\left(x-1\right)$ is a factor of $p\left(x\right)=k{x}^3-3x^2+5kx+10$.

If $\left(x+1\right)$ is a factor of $a{x}^3+x^2-2x+4a-9$, find the value of $a$.

If $\left(x-a\right)$ is a factor of $x^3-a{x}^2+2x+a-1$, find the value of $a$.

If $\left(x+2a\right)$ is a factor of $x^5-4a^2{x}^3+2x+2a+3$, find the value of $a$.