Question

Let f(x) = 12x5 − 36x4 − 6x3 and g(x) = 6x2. Find f of x over g of x.

2x2 + 6x + 1
2x2 − 6x − 1
2x3 + 6x2 + x
2x3 − 6x2 − x

Answer 1

The correct answer is choice 4.
You can factor f(x) to 6x^2(2x^3+6x^2-x)
Divide that by 6x^2 and you get choice 4.

Answer 2

For this case we have the following functions:

`f (x) = 12x ^ 5-36x ^ 4-6x ^ 3\\g (x) = 6x ^ 2`

We must find the value of:
`\frac {f (x)} {g (x)}`, then:

`\frac {f (x)} {g (x)} = \frac {12x ^ 5-36x ^ 4-6x ^ 3} {6x ^ 2} = \frac {12x ^ 5} {6x ^ 2} - \frac {36x ^ 4} {6x ^ 2} - \frac {6x ^ 3} {6x ^ 2}`

For division of powers of the same base, the same base is placed and the exponents are subtracted:

`\frac {f (x)} {g (x)} = 2x ^ 3-6x ^ 2-x`

Answer:

Option D