If the zero of the polynomial $p(x) = ax^2 - 11x + 3$ is $1$,then $a = \ldots$

What must be subtracted from $8x^4 + 14x^3 - 2x^2 + 8x - 12$ so that the resulting polynomial is exactly divisible by $4x^2 + 3x - 2$?

If the zeroes of the quadratic polynomial $x^{2}+(a+1)x+b$ are $2$ and $-3$,then

If one factor of $x^{3}+4 x^{2}+8 x+a$ is $(x+2)$,then find the value of $a$.

Find the zeroes of the following polynomial by the factorization method and verify the relationship between the zeroes and the coefficients of the polynomial:
$3x^2 + 4x - 4$

Identify the type of the following polynomial based on its degree: $p(x) = 7 - 5x$.