Question 30213
f(x) =3x^4-x^3-68x^2+76x+80
we have f(x) = 3x^4-x^3-68x^2+76x+80 
= (x-2)(3x^3+5x^2-58x-40)
=(x-2)[(x+5)(3x^2-10x-8)]
=(x-2)(x+5)(3x+2)(x-4)

We observe that x = 2,x = -5 and x = -2/3 are roots of f(x) = 0
The fourth root being 4 naturally x =2/3 CANNOT NOT satisfy f(x) = 0
(we can check by inspection and ascertain that it is not a root)
which means (3x-2) ISNOT A FACTOR of f(x)
Therefore (x+2),(x+5), (3x+2) are factors of f(x)

Answer: (c) 3x-2  IS NOT A FACTOR