Question

The expansion ${\left(x-\frac{x^2}{2}\right)}^{40}$ is a polynomial of $n^{th}$ degree in $x,$ then $n=$

• A. $20$
• B. $40$
• C. $80$
• D. $120$

Answer 1

Answer: (C)

$80$

$T_{r+1}={}^{40}{C}_r{x}^{40-r}{x}^{2r}{2}^{-r}$
The power of $x=40+r$
Highest power of $x$ occurs when $r=40$ (last term)
Hence, highest power of $x$ is $80.$
Hence, the polynomial is of degree $80.$