Evaluate $153 \times 147$.

Show that $p-1$ is a factor of $p^{10}-1$ and also of $p^{11}-1$.

Find the quotient and the remainder when $2x^2 - 7x - 15$ is divided by $2x - 3$.

Write whether the statement is True or False. Justify your answer.
The degree of the sum of two polynomials each of degree $5$ is always $5$.

Using the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 6$.

Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x + x^{2} - 1$
$(ii)$ $3x - 5$