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!