Which of the following is a quadratic polynomial?

Divide $x^{4}+4 x^{3}-2 x^{2}-12 x+9$ by $x^{2}-2 x+1$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0, a, b, c, d \in R)$ are $\alpha, \beta,$ and $\gamma$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Divide $x^{6}+5 x^{3}+7 x+3$ by $x^{2}+2$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$v^{2}+4 \sqrt{3} v-15$

Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the $x$-axis at exactly two points,it need not be a quadratic polynomial.