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

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Answer 1 · 2016-10-30T13:33:43

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!

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