document.write( "Question 1164256: Factorize the following: a^3+3a^2+3a+2 \n" ); document.write( "

Algebra.Com's Answer #788550 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The rational roots theorem tells us the only possible rational roots are 1, -1, 2, and -2.

\n" ); document.write( "Synthetic division shows us that -2 is a root:

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document.write( "  -2 | 1  3  3  2\r\n" );
document.write( "     |   -2 -2 -2\r\n" );
document.write( "     ------------\r\n" );
document.write( "       1  1  1  0

\n" ); document.write( "ANSWER: $\"a%5E3%2B3a%5E2%2B3a%2B2+=+%28a%2B2%29%28a%5E2%2Ba%2B1%29\"$

\n" ); document.write( "Here is a different path to the answer; this is what first caught my eye when I saw the problem.

\n" ); document.write( " $\"a%5E3%2B3a%5E2%2B3a%2B2+=+%28a%5E3%2B3a%5E2%2B3a%2B1%29%2B1+=+%28a%2B1%29%5E3%2B1%5E3\"$

\n" ); document.write( "Use the factorization pattern $\"x%5E3%2By%5E3+=+%28x%2By%29%28x%5E2-xy%2By%5E2%29\"$ :

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