Help find roots of a Polynomial Equation

Question

I'm trying to solve this one polynomial equation: x³ - 2x² + 10x + 136 = 0

 

I know the answer is apparently 3 +- 5i, -4 according to the answer guide but I'm unsure how to reach that conclusion.

 

I've gotten to the point where I have (x+4)(x²-6x+34) (which I believe is correct) but now im struggling to factor it out into intercept form. 

 

If someone could please explain this to me since I think I did something wrong, Thanks!

Answer 1

First, lets check if your factoring is correct.  Divide the polynomial by -4 using synthetic division.

 

-4 | 1       -2          10            136

 

               -4           24          - 136

______________________________

      1       -6           34             0

 

 

Since the remainder is zero, your factor is correct.

 

 

Then, you want to deal with that quadratic factor.   From there, just do what Timothy told you.

Answer 2

How about the Quadratic Formula?

I've tried it and it gives the two complex numbers!

Try it, yo'll like it.

Answer 3

Can't you just plug the trinomial into the quadratic formula?