Evaluate the following products without multiplying directly : $103 \times 107$
$11011$
$11021$
$11020$
$10021$
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)$ $\sqrt{2} x-1$