Factorize:

$x^2-32x-105$

Factorise: $x^2-11x-80$

Factorize: $6-x-x^2$

If we factorize: $x^2-\sqrt{3}x-6$ we get $\left(a+\sqrt{3}\right)\left(a-b\sqrt{3}\right)$. Find the value of $b$

Factorize:

$40+3x-x^2$

Factorise: $x^2-26x+133$

If we factorize: $x^2-2\sqrt{3}x-24$ we get $\left(a-b\sqrt{3}\right)\left(a+2\sqrt{3}\right)$. Find the value of $b$.

If we factorize: $x^2-3\sqrt{5}x-20$ we get $\left(k+z\sqrt{5}\right)\left(k+\sqrt{5}\right)$. Find the value of $z$

If the factors of $x^2+\sqrt{2}x-24$ are $\left(x-a\sqrt{2}\right)$ and $\left(x+b\sqrt{2}\right)$, then find the value of $\left(a+b\right)$ when $a$ and $b$ are positive.