How do you long divide # (2x^3 – 6x^2 – 14x – 1 ) /(3x + 1 )#?

1 Answer
Nov 7, 2015

Similar to long division of integers, proceed as described below to find:

#(2x^3-6x^2-14x-1)/(3x+1) = 2/3x^2-20/9x-106/27+(79/27)/(3x+1)#

Explanation:

Here I write out the coefficients of descending powers of #x# as sequences, then long divide:

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If you prefer, you can include the powers of #x# in the long division, but it makes no difference to the calculation.

Write the (coefficients of the) dividend #2x^3-6x^2-14x-1# under the bar and the (coefficients of the) divisor #3x+1# to the left.

Choose the first term of the quotient to match leading terms.
Multiply and subtract to get a remainder.
Bring down the next term from the dividend.
Repeat until left with a remainder of lower degree than the divisor.

We find:

#2x^3-6x^2-14x-1 = (3x+1)(2/3x^2-20/9x-106/27)+79/27#