document.write( "Question 269103: I am having trouble with factoring and solving. Please help. I will greatly appreciate it. Please show work.\r
\n" ); document.write( "\n" ); document.write( "Factor completely. If the polynomial is prime, state this.\r
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\n" ); document.write( " $\"-36x2+-+30x+%2B+36\"$ \r
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Algebra.Com's Answer #197236 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Don't list a bunch of problems.  We will only do one.\r\n" );
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document.write( "Factor completely by grouping. \r\n" );
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document.write( "Factor out -6, remembering that when you factor out \r\n" );
document.write( "a negative number, all the signs change inside the\r\n" );
document.write( "parentheses.\r\n" );
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document.write( "I'll do some coloring:\r\n" );
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document.write( "Ignoring signs at first, and just using absolute values,\r\n" );
document.write( "multiply the red 6 by the green 6, getting 36.\r\n" );
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document.write( "Now write down all the ways of two integers\r\n" );
document.write( "which multiply to give 36:\r\n" );
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document.write( "36*1 = 36\r\n" );
document.write( "18*2 = 36\r\n" );
document.write( "12*3 = 36\r\n" );
document.write( " 9*4 = 36\r\n" );
document.write( " 6*6 = 36\r\n" );
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document.write( "Now since the sign before the green 6 is -, out\r\n" );
document.write( "beside those we SUBTRACT the two factors. (If that sign\r\n" );
document.write( "has been + we would have added them):\r\n" );
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document.write( "36*1 = 36   36-1=35\r\n" );
document.write( "18*2 = 36   18-2=16\r\n" );
document.write( "12*3 = 36   12-3= 9 \r\n" );
document.write( " 9*4 = 36    9-4= 5\r\n" );
document.write( " 6*6 = 36    6-6= 0\r\n" );
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document.write( "Now we look in the right hand column to see if we can find\r\n" );
document.write( "the absolute value of the coefficient of the middle term of\r\n" );
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document.write( "which is 5, which I have colored green.\r\n" );
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document.write( "Now replace the 5x by 9x-4x \r\n" );
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document.write( "Now I'll do some re-coloring:\r\n" );
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document.write( "Out of the two red terms factor out a 3x\r\n" );
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document.write( "Now out of the remaining black terms, factor out ,\r\n" );
document.write( "remembering that when you factor out a negative you change\r\n" );
document.write( "the signs inside the parentheses:\r\n" );
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document.write( "Now I'll do some more re-coloring\r\n" );
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document.write( "Notice that the green parentheses are the same,\r\n" );
document.write( "and you can factor them out  just as you would\r\n" );
document.write( "factor out just a single letter or number.  When you do you just\r\n" );
document.write( "put the remaining black factors inside a parentheses:\r\n" );
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document.write( "or just\r\n" );
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document.write( "Edwin

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