Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $x^{2}+x$
$(ii)$ $x-x^{3}$
$(iii)$ $y+y^{2}+4$
$(i)$ $x^{2}+x$
$\because $ The degree of $x ^{2}+ x$ is $2$ . $\therefore $ It is a quadratic polynomial.
$(ii)$ $x-x^{3}$
$\because$ The degree of $x-x^{3}$ is $3$. $\therefore$ It is a cubic polynomial.
$(iii)$ $y+y^{2}+4$
$\because$ The degree of $y+y^{2}+4$ is $2$ $\therefore$ It is a quadratic polynomial.
Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x -1$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{3}+x^{2}+x+1$.
Evaluate the following products without multiplying directly : $104 \times 96$
Find the zero of the polynomial : $p(x)=a x,\,\, a \neq 0$