Let f(x) = 2x^3 + x^2 - 5x + c. Given that f(1) = 0 find the values of c.

In order to solve this question we simply must substitute x=1 into f(x).

If we carry out this substitution we see that

f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1  - 5 + c = 3 - 5 + c = c - 2.

We also know from the question provided that f(1) = 0. We can therefore match this condition with the substitution that we have just made which allows us to make the following statement. f(1) = c - 2 = 0.

We can then rearrange this equation in order to get an expression for c by adding 2 to both sides, therefore c = 2.