The polynomials $2x^3-7x^2+ax-6$ and$x^3-8x^2+(2a+1)x-16$ leave the same remainder when divided by $\mathrm{x}-2$. Find the value of $\text{'}\mathrm{a}\text{'}$.

If$(\mathrm{x}-2)$ is a factor of the expression$2x^3 +a{x}^2+bx-14$ and when the expression is divided by$(\mathrm{x}-3)$, it leaves a remainder $52$, find the values of $\mathrm{a}$ and$\mathrm{b}$.

Find$\text{'}\mathrm{a}\text{'}$ if the two polynomials $a{x}^3+3x^2-9$ and $2x^2+4x+a$, leave the same remainder when divided by$\mathrm{x}+3$.

Using the Factor Theorem, show that :

 $(\mathrm{x}-2)$ is a factor of $x^3-2x^2-9x+18$. Hence, factorise the expression $x^3-2x^2-9x+18$completely.

Using the Factor Theorem, show that :

 $(\mathrm{x}+5)$ is a factor of $2x^3+5x^2-28x-15$. Hence, factorize the expression $2x^3+5x^2-28x-15$ completely.

Using the Factor Theorem, show that :

 $(3\mathrm{x}+2)$ is a factor of $3{\mathrm{x}}^3+2{\mathrm{x}}^2-3\mathrm{x}-2$. Hence, factorize the expression $3{\mathrm{x}}^3+2{\mathrm{x}}^2-3\mathrm{x}-2$ completely.

Using the Remainder Theorem, factorize each of the following completely : 

$3x^3+2x^2-19x+6$

Using the Remainder Theorem, factorize each of the following completely : 

$2x^3+x^2-13x+6$

Using the Remainder Theorem, factorise each of the following completely : 

$3x^3+2x^2-23x-30$