X^4 - 1 (x - 1) (x + 1) (x + i) (x - i)

(x - 1) (x - 1) (x - i) (x - i)

(x - 1) (x + i)

(x^2 - 1) (x^2 + 1)

9514 1404 393

  (a)  (x - 1) (x + 1) (x + i) (x - i)

Step-by-step explanation:

Perhaps you want the fully factored form.

The difference of squares is factored as ...

  a² -b² = (a -b)(a +b)

Your expression can be considered to be the difference of squares ...

  (x²)² -(1)² = (x² -1)(x² +1)

Each of these factors can be considered to be the difference of squares:

  x² -1 = (x -1)(x +1)

  x² +1 = x² -(i²) = (x -i)(x +i)

So, the fully factored form is ...

  x^4 -1 = (x -1)(x +1)(x -i)(x +i)

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).