document.write( "Question 292165: How would I solve this polynomial division problem? \r
\n" ); document.write( "\n" ); document.write( "(24x^3 + 3) / (2x + 1) \n" ); document.write( "

Algebra.Com's Answer #211120 by Earlsdon(6294) $\"\"$ $\"About$

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Well, you have a couple of choices:
\n" ); document.write( "1) You could divide using long division or synthetic division.
\n" ); document.write( "2) You could try factoring the numerator and see if anything will cancel the denominator.
\n" ); document.write( "Let's try 2)
\n" ); document.write( " $\"%2824x%5E3%2B3%29%2F%282x%2B1%29\"$ Factor 3 from the numerator.
\n" ); document.write( " $\"3%288x%5E3%2B1%29%2F%282x%2B1%29\"$ Now factor the binomial in the numerator as the sum of two cubes.
\n" ); document.write( " $\"3%288x%5E3%2B1%29+=+3%28highlight_green%28%282x%29%5E3%2B%281%29%5E3%29%29\"$
\n" ); document.write( "Recall that the sum of two cubes will factor thus:
\n" ); document.write( " $\"A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\"$ and here, A = 2x, B = 1, so...
\n" ); document.write( " $\"3%288x%5E3%2B1%29+=+3%282x%2B1%29%284x%5E2-2x%2B1%29\"$ so now we have:
\n" ); document.write( " $\"3cross%28%282x%2B1%29%29%284x%5E2-2x%2B1%29%2Fcross%28%282x%2B1%29%29\"$ = $\"3%284x%5E2-2x%2B1%29+=+highlight%2812x%5E2-6x%2B3%29\"$ \n" ); document.write( "

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