Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $3 \sqrt{t}+t \sqrt{2}$
$3 \sqrt{t}+t \sqrt{2}$
$\Rightarrow 3 t^{1 / 2}+\sqrt{2} \cdot t$
$\because $ $\frac{1}{2}$ is not a whole number,
$\therefore $ $3 t^{1 / 2}+\sqrt{2} \cdot t,$ i.e. $3 \sqrt{t}+t \cdot \sqrt{2}$ is not a polynomial.
Factorise : $x^{3}+13 x^{2}+32 x+20$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+3 x^{3}+3 x^{2}+x+1$.
Write $(3a + 4b + 5c)^2$ in expanded form.
Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $5+2 x$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.