Question

(x^(5)+15x^(4)+54x^(3)-25x^(2)-75x-34) / (x+8)

Answer 1

`x^(4)+7x^(3)-2x^(2)-9x-3-(10)/(x+8)`

Step-by-step explanation

We want to divide the given expression by x + 8:

`x^5+15x^4+54x^3-25x^2-75x-34`

To do this, first, divide the term by x, and then multiply the result by 8. Then, subtract this from the rest of the terms in the expression and repeat for each term.

Let us do that:

As we can see, the remainder in the division is -10.

Therefore, the answer is:

`x^4+7x^3-2x^2-9x-3-(10)/(x+8)`