By Remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where

$p(x)=x^{3}-2 x^{2}-4 x-1, \quad g(x)=x+1$

$4 x^{2}+11 x-3$ is a $\ldots \ldots . .$ polynomial.

Write whether the following statements are True or False. Justify your answer.

$\frac{6 \sqrt{x}+x^{\frac{3}{2}}}{\sqrt{x}}$ is a polynomial, $x \neq 0$

Divide $p(x)=21+10 x+x^{2}$ by $g(x)=2+x$ and find the quotient and the remainder.

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x-6$

Factorise the following quadratic polynomials by splitting the middle term

$x^{2}+10 x+16$