Question

Let P(x) be a polynomial with degree 2017 and leading co-efficient unity such that P(0) = 2016, P(1) = 2015, P(2) = 2014,….P(2016) = 0 then the value of P(2017) = n! - a where n and a are natural number then value of (n + a)

• A. 2018
• B. 2017
• C. 2019
• D. 2016

Answer 1

The correct option is A 2018

$P\left(x\right)-2016+x=x(x-1)(x-2)(x-3)\dots \dots (x-2016)$
Put $x=2017$
P(2017) + 1 = (2017)!