Find the values of $a$ and $b$ so that the polynomial $(x^3-10x^2+ax+b)$ is exactly divisible by $(x-1)$ as well as $(x-2).$

Draw the graphs of linear equations $y=x$ and $y=-x$ on the same cartesian plane. What do you observe?

$p\left(x\right)=x^3-3x^2+4x+50, g\left(x\right)=x-3$

$p\left(x\right)=x^3-6x^2+2x-4, g\left(x\right)=1-\frac{3}{2}x$

If $x+\frac{1}{x}=6$, then the value of $x^2+\frac{1}{x^2}$ is