X^3-7x^2-x+7=0 make a list of possible roots, write the resulting quadratic function, factor or use quadratic formula to find the final 2 roots

( - 1) ³ - 7 · ( - 1) ² - ( - 1) + 7 = - 1 - 7 + 1 + 7 = 0

The first possible root is x 1 = - 1 and (x + 1) is a factor:

x³ - 7 x² - x + 7 = (x + 1) (x² - 8 x + 7) = 0

x² - 8 x + 7 = x² - 7 x - x + 7 = x (x - 7) - (x - 7) = (x - 7) (x - 1) = 0

Final 2 roots are: x 2 = 1, x 3 = 7.