#5. looks fine. The roots are { +√(6) , -√(6) , -2, 2 }
#6. 12x³ + 26x² - 10x factor out 2x 2x(6x² + 13x - 5) = 0 one root is zero
factor for other two roots, only 5×1 = 5 (3x-1)(2x+5) 3x - 1 = 0 3x = 1 x = 1/3
2x + 5 = 0 2x = -5 x = -5/2
roots are { 0, 1/3, -5/2 }
EDIT** forgot #7
#7. 125x³ + 8 = 0
125x³ = -8 x³ = -8/125 x = ∛(-8/125)
root of a fraction is the root of the numerator and denominator, negative can be on either numerator or denominator. overall fraction should be negative to subtract from the 8 to give zero.