Question

How do you simplify and divide `(y^5+32)(y+2)^-1`?

Answer 1

Let's start by simplifying, using the rule `a^-1 = 1/a`.

`=> (y^5 + 32)/(y + 2)`

This is now a division problem, that can be done by either synthetic or long division. I will do it using synthetic division.

`-2"_|1 0 0 0 0 32"`
`" -2 4 -8 16 -32"`
`"-----------------------------------------------------------"`
`" 1 -2 4 -8 16 0"`

So, the quotient is `y^4 - 2y^3 + 4y^2 - 8y + 16`.

This cannot be factored further, if you check using the rational root theorem and the remainder theorem.

Hopefully this helps!