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

Find the value of each of the following polynomials at the indicated value of variables : $p(t)=4 t^{4}+5 t^{3}-t^{2}+6$ at $t=a$.

Find $p(0)$, $p(1)$ and $p(2)$ for  of the following polynomials : $p(y)=y^{2}-y+1$

Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x+1$

Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x$.

Evaluate $105 \times 106$ without multiplying directly.