Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+7 x-20$

Factorise

$6 x^{3}+7 x^{2}-14 x-15$

Which of the following expressions is a polynomial, state the reason ? If an expression is polynomial, state whether it is a polynomial in one variable or not

$5 x^{2}+11 x-2 \sqrt{x}$

If $x^{51}+51$ is divided by $x+1,$ the remainder is

Examine whether $2 x+3$ is a factor of $2 x^{3}+21 x^{2}+67 x+60$ or not.