What are all the possible rational zeros for f(x)=6x3+6x2−15x−2f(x)=6x3+6x2−15x−2?

Answer 1

y = 6x^3 + 6x^2 - 15x - 2

p = {+-1, +-2}

q = {+1,+-2,+-3,+-6}

p/q = {+-1, +-1/2, +-1/3 , +-1/6, +-2,+-2/3}

This is the list of possible rational zeros and NONE of them work!!!

So it must be solved numerically (by examining the graph)

The irrational solutions are (APPROXIMATELY)

x = -2.11, x = -0.128, x=1.238

Answer 2

You find all numbers that go into the constant -2. Which are +/- 1 and +/- 2

Then you find all numbers that go into the leading coefficient, 6. They are +/-1, +/-2, +/-3 and +/-6

Now you form all fractions where the numerator comes from the factors of -2 and where the denominators come from the factors of 6

You get +/-1, +/- 1/2, +/- 1/3, +/- 1/6, +/- 2, +/- 2/3

That last list has all the possible rational zeros