Question

The coefficient of $x^9$ in $(x-1)(x-4)(x-9).....(x-100)$ is

• A. $-235$
• B. $235$
• C. $385$
• D. $-385$

Answer 1

The correct option is D $-385$

There are $10$ factors. $x^9$ requires one $x$ from $9$ factors and multiplied by one of the numbers involved.

So coefficient of ${}^9$ is

$-(1^2+2^2+3^2+\dots +\dots \dots \dots +9^2+{10}^2)$

$=-{\sum }_{r=1}^{10}{r}^2$

$=-\frac{-10\times (10+1)\times (2\times 10+1)}{6}=-385$ Option D