$P(x) = 4x^{3} + 3x^{2} + 2x + 1$ is a $\ldots$ polynomial.

Draw the graph of $p(x) = 3 - 2x - x^2$ and find the zeros of this polynomial.

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

The product of two polynomials is $x^{3}-3x^{2}-x+3$ and one of the polynomials is $x+1$. Find the other polynomial.

From the following figure,find the number of zeros of $y=p(x)$ :

Are the following statements 'True' or 'False'? Justify your answers.
The only value of $k$ for which the quadratic polynomial $k x^{2}+x+k$ has equal zeros is $\frac{1}{2}$.