If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$

Classify the following as linear, quadratic or cubic polynomial

$x^{3}+5 x^{2}+12$

The polynomial $p(x)=x^{4}-2 x^{3}+3 x^{2}-a x+3 a-7$ when divided by $x+1$ leaves the remainder $19 .$ Find the values of $a .$ Also find the remainder when $p(x)$ is divided by $x+2.$

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

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

From the following polynomials find out which of them has $(x-1)$ as a factor

$x^{3}-7 x^{2}+14 x-8$