Give an example of a polynomial, which is:
$(i)$ monomial of degree $1$
$(ii)$ binomial of degree $20$
$(iii)$ trinomial of degree $2$
We know that a polynomial having only one term is called a monomial, a polynomial having only two terms is called binomial, a polynomial having only three terms is called a trinomial.
$(i)$ $3 x$ is monomial of degree $1 .$
$(ii)$ $x^{20}-7$ is a binomial of degree $20 .$
$(iii)$ $5 x^{2}+3 x-1$ is a trinomial of degree $2 .$
If $x-2$ is a factor of $x^{3}-3 x^{2}+a x+24$ then $a=\ldots \ldots \ldots$
Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x+x^{2}-1$
$(ii)$ $3 x-5$
By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where
$p(x)=4 x^{3}-12 x^{2}+14 x-3, g(x)=2 x-1$
Factorise
$49 x^{2}-35 x+6$