Question

Which of the following is a factor of f(x) = 3x3 + 8x2 − 87x + 28?

Answer 1

Answer: (x-4)

I just took the test and that's the answer. I can't explain it though.

Answer 2

Factoring a trinomial is a tedious process, sometimes involving a trial-and-error process. The best approach would be to try out all the choices, replace them with x, and see if it satisfies the equation to be equal to zero. Since no choice are given, we use another technique: by using the scientific calculator under mode EQN (equation).

Once you're in mode EQN, choose the trinomial (ax^3 + bx^2 +cx +d =0).Then, all you have to do is substitute the coefficients (a=3, b = 8, c = -87, d = 28). Press equals, then the three roots would appear. 

The roots, and therefore factors, are -7, 4 and 1/3. Any of those are factors of the given equation.