# Dealing with polynomials

If the 5 degree polynomial has a leading coefficient of 2009,where

f(1) = 1, f(2) = 3, f(3) = 5, f(4) = 7, and f(5) = 9,

then what is the value of f(8)?

• Did you try solving for the coefficients of the polynomial? You have five equations and five unknowns.. it's not hard to solve.. – Cameron Williams Oct 14 '16 at 18:52
• And one coefficient is already given. – piepi Oct 14 '16 at 18:59

Let $q(x)=f(x)-(2x-1)$ which is of 5th degree with roots $1,2,3,4,5$ and it's leading term is $2009$ so:
$q(x)=2009(x-1)(x-2)(x-3)(x-4)(x-5)=f(x)-(2x-1)$ so from here you can calculate as
$2009(8-1)(8-2)(8-3)(8-4)(8-5)=f(8)-(2\cdot 8 -1)$