Expand $(2 x-3)(2 x+5)$.

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

For the polynomial $p(x),$ if $p(7)=0,$ then $\ldots$ is a factor of $p(x).$

Factorise: $x^{3}+x^{2}-4x-4$

Write the coefficient of $x^{2}$ in the following polynomial: $\sqrt{3} x^{2}+11$.

Show that $2x - 3$ is a factor of $x + 2x^3 - 9x^2 + 12$.