Obtain the quadratic polynomial in the standard form with the following coefficients: $a=1, b=-10, c=25$.

Verify that $3$ is a zero of the linear polynomial $p(x) = 4x - 12$.

What must be added to the polynomial $p(x) = 6x^5 + 5x^4 + 11x^3 - 3x^2 + x + 1$ so that the resulting polynomial is exactly divisible by $3x^2 - 2x + 4$? (Hint: add $-r(x)$ to $p(x)$)

If the sum of the zeros is $-3$ and the product of the zeros is $-4,$ then the quadratic polynomial is $\ldots \ldots \ldots$

The value of $p(x) = 3x^2 + 7x + 4$ at $x = 1$ is:

Prove that $1/2, 1$ and $-2$ are the zeros of the cubic polynomial $p(x) = 2x^3 + x^2 - 5x + 2$. Also,verify the relationship between the zeros and the coefficients.