SOLUTION: Question: Use the factor between therorm to determin whichofhte following is not a factor of f(x) =3x^4-x^3-68x^2+76x+80 Possible Answer: (a) a-2 (b) 3x+2 (c) 3x-2 (d) x+5

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Question 30213: Question:
Use the factor between therorm to determin whichofhte following is not a factor of f(x) =3x^4-x^3-68x^2+76x+80
Possible Answer:
(a) a-2
(b) 3x+2
(c) 3x-2
(d) x+5
Please be specific in which possible answer is correct. thank you!!!
Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website!
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