Question

If the degree of the polynomial $(p^6+\frac{3}{7})(p^n+3p)$ is $9$ then the value of $n$ is

• A. $1$
• B. $3$
• C. $6$
• D. $18$

Answer 1

The correct option is B $3$

$(p^6+\frac{3}{7})(p^n+3p)$
$=p^6\times p^n+p^6\times 3p+\frac{3}{7}{p}^n+\frac{3}{7}\times 3p$

$=p^{6+n}+3p^7+\frac{3}{7}{p}^n+\frac{9}{7}p$

$\therefore$ Degree $=9$ $\Rightarrow$ Highest power of $p=9$
Term containing highest power $=p^{6+n}$
$6+n=9\Rightarrow n=3$