
Mark H. answered 01/27/20
Tutoring in Math and Science at all levels
Start by factoring out the x to get:
x^4 - 12x^3 + 54x^2 - 108x - 175 (there is a zero at x = 0)
Next, factor 175 to get 7*5*5
Try a factor of (x - 7).....using long division, the result is:
x^3 - 5x^2 + 19x + 25
This has 3 factors, so write the 3 factors of 25: 5,5,1
Try a factor of x + 1. Using long division, the result is:
x^2 - 6x + 25
This is not factorable, and the last 2 roots will be complex (since b^2 - 4ac is negative)
So, the real roots are 0, 7, and -1. If you need the complex roots, use the quadratic formula.
Note: I used a graphing calculator to get my apparently lucky guesses