Find the value of the polynomial $p(x) = 5x - 4x^2 + 3$ at $x = 2$.

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer: $3 \sqrt{t} + t \sqrt{2}$

Classify the following as linear,quadratic,and cubic polynomials:
$(i)$ $1+x$
$(ii)$ $3t$
$(iii)$ $r^{2}$
$(iv)$ $7x^{3}$

Find the value of $k$, if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = 2x^2 + kx + \sqrt{2}$.

Write the following cube in the expanded form: $(3a + 4b)^3$

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