How do you divide #( -3x^3 + 5x + 14) div (x-2)#?

1 Answer
Feb 14, 2017

#-3x-1 + (16/(x-2))#

Explanation:

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diving by long division, you want to try and eliminate each term in the dividend (#-3x^2 + 5x + 14)# one by one until you get a remainder that you can no longer divide by

we multiply #(x-2)# by #(-3x)# to get #(-3x^2+6x)#, and then we subtract it from the dividend #(-3x^2 + 5x + 14)# to get #(-x)#

we keep doing this until we get a remainder that we can no longer divide by

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there's nothing that you can multiply by #(x-2)# that can make it any simpler, 16 is as far as we go

so now you have a quotient #(-3x-1)# and your remainder #(16)/(x-2)#
so your answer is #-3x-1 + (16/(x-2))#