If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.
$11$
$3$
$-1$
$4$
The following expressions are polynomials? Justify your answer:
$\frac{1}{2 x}$
Find the following products:
$\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)$
If $x+1$ is a factor of $a x^{3}+x^{2}-2 x+4 a-9,$ find the value of $a$.
Factorise the following quadratic polynomials by splitting the middle term
$12 x^{2}+23 x+5$
Write the following cubes in expanded form
$(3 x+2 y)^{3}$
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