document.write( "Question 1172699: How would you factor a polynomial? My equation is
\n" ); document.write( "3x^2+4x+1
\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #797822 by greenestamps(13215)\"\" \"About 
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\n" ); document.write( "If it is factorable, then it is the product of two linear factors:

\n" ); document.write( "\"%28ax%2Bb%29%28cx%2Bd%29+=+%28ac%29x%5E2%2B%28bc%2Bad%29x%2Bbd\"

\n" ); document.write( "where a, b, c, and d are integers.

\n" ); document.write( "You want the product to be 3x^2+4x+1

\n" ); document.write( "Equating coefficients, that means...
\n" ); document.write( "(1) ac=3
\n" ); document.write( "(2) bc+ad=4
\n" ); document.write( "(3) bd=1

\n" ); document.write( "The only way for ac=3 to be a product of two integers is if a and c are 1 and 3.
\n" ); document.write( "The only way for bd=1 to be a product of two integers is if b and d are both 1.

\n" ); document.write( "That make the only possible factorization

\n" ); document.write( "\"3x%5E2%2B4x%2B1+=+%28x%2B1%29%283x%2B1%29\"

\n" ); document.write( "That factorization give us the right coefficient for the middle term: bc+ad = 1(3)+1(1) = 3+1 = 4.

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