[(x^3n)-(3x^2n)+(5x^n)-6]÷ [(x^n)-2]

Question

Here is the question: Assuming n is a positive integer, divide [ (x^3n) - (3x^2n) + (5x^n) - 6 ]÷ [ (x^n) - 2 ]

Please Show work so I can understand the solution better.

Answer 1

Let x^n = y.

Then, we are solving (y^3 - 3y^2 + 5y - 6)/(y - 2)

Use synthetic division with 2.

2 | 1 -3 5 -6

2 -2 6

1 -1 3 0

Thus, we have (y^3 - 3y^2 + 5y - 6)/(y - 2) = y^2 - y + 3

Substituting x*n for y, we have x^2n - x^n + 3

Answer 2