Identify the type of the given polynomial based on its degree: $p(x) = 3.14x^2 + 1.57x + 1$.

Identify the type of the given polynomial based on its degree: $p(x) = 9x^{2} + \frac{7}{2}x^{3} + 5$.

For the given sum and product of zeroes,find the quadratic polynomial. Also,find the zeroes of this polynomial by factorization:
Sum of zeroes = $-2 \sqrt{3}$,Product of zeroes = $-9$.

Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

Answer the following and justify: What will be the quotient and remainder on division of $ax^{2} + bx + c$ by $px^{3} + qx^{2} + nx + s$,where $p \neq 0$?

$A$ dealer bought $x^{2}+2x+3$ pieces of mobiles for Rs. $x^{3}+6x^{2}+11x+12$. Find the price of one mobile.