How do you divide #(3x^3 + 17x^2 + 15x + 2) # by #x+5#?

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Answer 1 · 2018-03-20T01:19:49

#3x^2+2x+5-(8)/(x+5)#

General process: multiply #x+5# by a quantity that allows you to match the largest power of #x# term in the quantity inside.

So the first step, you would do #(x+5)xx3x^2# in order to produce the term #3x^3#.

Similarly, in the second step you do #(x+5)xx2x# to match #2x^2#.

The third step you do #(x+5)xx5# to produce #5x#.

Since #-8# is an #x^0# term, this is less than the #x^1# term in #x+5#. So this where we stop. #-8# becomes the remainder.

I have colored various quantities to show how the answer is put together after the division.

I apologize for the trackpad handwriting.