If f(x) = x^3 – x^2 – 3, which of the following is equal to g(x) = f(2 – x)? –x^3 + 5x^2 – 8x + 1 –x^3 + 7x^2 – 16x – 15 x^3 + 5x^2 + 8x + 1 x^3 – 7x^2 + 16x – 15

–x^3 + 5x^2 – 8x + 1

Step-by-step explanation:

You can observe that expanding f(2-x) will give you a sum that includes (2-x)³, so will have a -x³ term. This narrows the choices to one of the first two.

If x=0, then you have ...

... f(2) = 2^3 -2^2 -3 = 8 - 4 - 3 = 1 . . . . corresponds to the first selection

Worked in detail

f(2-x) = (2-x)³ -(2-x)² -3 . . . . substitute 2-x for x in the expression for f(x)

... = (2³ -3·2²x +3·2x² -x³) -(2² -2·2x +x²) -3

... = -x³ +5x² -8x +1 . . . . . matches the first selection

Using ...

... (a+b)³ = a³ + 3a²b +3ab² +b³

... (a+b)² = a² +2ab +b²

mk./km: lm

step-by-step explanation:

,mlmlm

; mk

lk

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.