Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $1+x$
$(ii)$ $3 t$
$(iii)$ $r^{2}$
$(iv)$ $7 x^{3}$
$(i) $ $1+x$
$\because$ The degree of $1+x$ is $1$ $\therefore$ It is a linear polynomial.
$(ii)$ $3 t$
$\because$ The degree of $3 t$ is $1 .$ $\therefore$ It is a linear polynomial.
$(iii)$ $r^{2}$
$\because$ The degree of $r^{2}$ is $2$ $\therefore$ It is a quadratic polynomial.
$(iv)$ $7 x^{3}$
$\because$ The degree of $7 x ^{3}$ is $3 .$ $\therefore$ It is a cubic polynomial.
Find the value of $k,$ if $x-1$ is a factor of $4 x^{3}+3 x^{2}-4 x+k$.
Find the value of the polynomial $5x -4x^2+ 3$ at $x = -\,1$.
Evaluate the following using suitable identities : $(102)^{3}$
Find the remainder when $x^{3}-a x^{2}+6 x-a$ is divided by $x-a$.
Factorise : $2 y^{3}+y^{2}-2 y-1$