Question:
For the polynomial $\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6}$, then write
(i) the degree of the polynomial
(ii) the coefficient of $x^{3}$
(iii) the coefficient of $x^{6}$
(iv) the constant term
Solution:
Given, polynomial is, $\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6}$
$=\frac{1}{5} x^{3}+\frac{2 x}{5}+\frac{1}{5}-\frac{7}{2} x^{2}-x^{6}$
(i) Degree of the polynomial is the highest power of the variable $i, e, 6 .$
(ii) The coefficient of $x^{3}$ in given polynomial is $\frac{1}{5}$.
(iii) The coefficient of $x^{6}$ in given polynomial is $-1$.
(iv) The constant term in given polynomial is $\frac{1}{5}$,