Suppose f is a quadratic function given by f(x) = ax^2 +bx + c, where...

Suppose f is a quadratic function given by f(x) = ax^2 +bx + c, where a,b and c are real numbers and we assume that a is not equal to zero.
If 0 is a root of f, explain why c = 0, or , in other words, why ax^2 +bx + c is evenly divisible by x.
f(x) = ax^2+bx+c since 0 is root of f f(0) = 0
f(0) = a*0^2+b*0+C =0 => c =0
f(x) = ax^2+bx = x(ax+b) so f(x) is evenly divisible by x.