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)

(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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