document.write( "Question 232377: Factor completely\r
\n" ); document.write( "\n" ); document.write( "-x^2+10x-21/-3x^2+23y-14 \n" ); document.write( "
Algebra.Com's Answer #171741 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Whenever you are factoring, keep an eye out for factoring out a -1. It can always be done and sometimes doing so makes a problem easier. Since factoring trinomials is easier with a positive leading coefficient, I am going to start by factoring out -1:
\n" ); document.write( "\"%28-x%5E2%2B10x-21%29%2F%28-3x%5E2%2B23y-14%29\"
\n" ); document.write( "\"%28%28-1%29%28x%5E2-10x%2B21%29%29%2F%28%28-1%29%283x%5E2-23y%2B14%29%29\"
\n" ); document.write( "The trinomials are now easier to factor, especially the first one. The second one is a bit more difficult. Since 3 factors in only one way, 3 = 3*1, the factors will look like:
\n" ); document.write( "(3x )(x )
\n" ); document.write( "if it factors at all. And since the 14 is positive and the 23 is negative, the factors will look like:
\n" ); document.write( "(3x - )(x - )
\n" ); document.write( "Now we just have to figure out which factors of 14 (1 and 14 or 2 and 7) to use and where to place them in the above so that we would end up with 23 in the middle if you we to multiply.
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\n" ); document.write( "Now we can cancel common factors:
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\n" ); document.write( "leaving
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\n" ); document.write( "(NOTE: Do not cancel the x's or the 3's here. They are not factors!)\r
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