Factor Theorem

Use factor theorem to factorise $6x^3+17x^2+4x-12$  completely.

Using the factor theorem, show that $\left(x-2\right)$ is a factor of $x^3+ x^2– 4x–4$. Hence, factorize the polynomial completely.

Use remainder theorem to factorize the following polynomial:

 $2x^3+3x^2-9x-10$

If $\left(x+2\right)$ and $\left(x+3\right)$ are factors of $x^3+ax+b,$find the values of $\text{'}a\text{'}$ and $\text{'}b\text{'}$.