document.write( "Question 116510: Rewrite the middle term as the sum of two terms and then factor completely.
\n" ); document.write( "12 $\"w%5E2\"$ +19w+4 \n" ); document.write( "

Algebra.Com's Answer #84726 by jgr45(31) $\"\"$ $\"About$

You can put this solution on YOUR website!
12 $\"w%5E2\"$ +19w+4\r
\n" ); document.write( "\n" ); document.write( "To factor this we need to find factors of 4 that sum to 19 after multiplying one or both of the factors by 2,3,4,6, or 12. The 9 possibilites are as follows:\r
\n" ); document.write( "\n" ); document.write( "(12w+2)(w+2) 24w+2w=26w, no good
\n" ); document.write( "(6w+2)(2w+2) 12+4=16, no
\n" ); document.write( "(4w+2)(3w+2) 8+6=14, no
\n" ); document.write( "(12w+4)(w+1) 12+4=16, no
\n" ); document.write( "(6w+4)(2w+1) 6+8=14, no
\n" ); document.write( "(4w+4)(3w+1) 4+12=16, no
\n" ); document.write( "(12w+1)(w+4) 48+1=49, no
\n" ); document.write( "(6w+1)(2w+4) 24+2=26, no
\n" ); document.write( "(4w+1)(3w+4) 16+3=19, AHA!!!\r
\n" ); document.write( "\n" ); document.write( "So the correct factorization is (4w+1)(3w+4). \n" ); document.write( "

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