Two factors of a polynomial $P\left(x\right)=x^3-19x-30$ are $\left(x+2\right)$ and $\left(x+3\right)$

The third factor of $P\left(x\right)$ is .

Use remainder theorem to factorize the following polynomial:

 $2x^3+3x^2-9x-10$

Following two statements speak about Arithmetic Progression.

Statement (A) : In an Arithmetic Progression series: $20+19\frac{1}{3}+18 \frac{2}{3} +$......................... $25$ terms is $300$

Statement (B) : In an Arithmetic Progression series : $20+19\frac{1}{3}+18\frac{2}{3}+$......................... $36$ terms is $300$

Pick the correct option from below:

If $x^{100}+2x^{99}+k$ is fully divisible by $\left(x+1\right)$ then value of $k$ will be:

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 $\text{'}b\text{'}$.