Evaluate the following products without multiplying directly : $103 \times 107$

Find the remainder obtained on dividing $p(x)=x^3+1$ by $x+1$.

Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=2 x^{2}+k x+\sqrt{2}$

Find the following products using appropriate identities :

$(i) $ $ (x + 3) (x + 3)$

$(ii)$ $(x -3) (x + 5)$

Verify whether the following are zeroes of the polynomial, indicated against them.

$p(x)=5 x-\pi, \,\,x=\frac{4}{5}$

Write the coefficients of $x^2$ in each of the following : 

$(i)$ $\frac{\pi}{2} x^{2}+x$               $ (ii)$ $\sqrt{2} x-1$