One root of f (x) = x^3-4x^2-20+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

A. (x + 6) (x + 8)

B. (x - 6) (x - 8)

C. (x - 2) (x + 4) (x - 6)

D. (x + 2) (x - 4) (x + 6)

Answer: (x-2) (x+4) (x-6)

Step-by-step explanation:

Since it is given that x=6 is the root of the given polynomial, hence x-6 is its one of the factors. Thus A and D are rejected. Now as it is a cubic polynomial, it should have 3 roots and thus 3 factors, they can be repeated. Thus option B is rejected. Hence we need to check option C. As x-2 is a factor then f (2) should be 0.

f (2) = 8-16-40+48=0

6 is already a root. As x+4 is a factor, we need to check if f (-4) = 0 or not.

f (-4) = - 64-64+80+48=0

Hence C is correct

c

Step-by-step explanation:

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