How do you simplify #(2x^3-14x+2 )/(x+3)#?

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Answer 1 · 2015-06-21T22:17:44

I agree with Jim that the expression maybe should have been

#(2x^3-14x+12) / (x+3)#,

but let's see what happens with the one given...

#(2x^3-14x+2) / (x+3)#

#=(2x^3+6x^2-6x^2-18x+4x+12-10) / (x+3)#

#=((2x^2-6x+4)(x+3)-10) / (x+3)#

#=2x^2-6x+4 - 10/(x+3)#

#=2(x-2)(x-1) - 10/(x+3)#

This doesn't really tell you much more than the original expression, and is not noticeably simpler.

It would be helpful if that #-10/(x+3)# remainder term were not there,

which is what would happen if the numerator were

#2x^3-14x+12#