A two digit positive number is such that the product of its digits is $6 .$ If $9$ is added to the number, the digits interchange their places. Find the number.

Factorise $a^2\left(b+c\right)+b^2\left(c+a\right)+c^2\left(a+b\right)+3abc$.

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