Find the value of $k$ of the polynomial $P\left(x\right)=2x^2-6x+k$, such that the sum of zeros of it is equal to half of the product of their zeros.

If the polynomial $p\left(x\right)=x^2-x+1$ is divided by $\left(x-2\right)$ then the remainder is 

Write the degree of the polynomial $f\left(x\right)=x^2-3x^3+2$

Find the quotient and the remainder when $f\left(x\right)=2x^3-3x^2+5x-7$ is divided by $g\left(x\right)=\left(x-3\right)$ using synthetic division.

The sum and product of the zeroes of a quadratic polynomial $P\left(x\right)=a{x}^2+bx+c$ are $-3 \& 2$ respectively. Such that $b+c=5a$.

Find the quotient and the remainder when $P\left(x\right)=3x^3+x^2+2x+5$ is divided by $g\left(x\right)=x^2+2x+1$.