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

If the sum of the zeros is $-7$ and the product of the zeros is $12$,then the quadratic polynomial is $\ldots \ldots \ldots$

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$7 y^{2}-\frac{11}{3} y-\frac{2}{3}$

The standard form of a quadratic polynomial of one variable is $\ldots .$

Prove that $-6, -\frac{1}{2}$ and $1$ are the zeros of the cubic polynomial $p(x) = 2x^3 + 11x^2 - 7x - 6$. Also,verify the relationship between the zeros and the coefficients.

Verify that the numbers given alongside the cubic polynomials below are their zeroes. Also,verify the relationship between the zeroes and the coefficients in each case: $2x^3 + x^2 - 5x + 2; \frac{1}{2}, 1, -2$.