document.write( "Question 250004: Factor 3z^2+14z +8\r
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Algebra.Com's Answer #182001 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
hFactor 3z^2+14z +8 \r
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document.write( "We try to factor it.\r\n" );
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document.write( "Multiply the 3 by the 8, get 24.  Write down all the ways\r\n" );
document.write( "you can multiply two positive integers together to get 24.\r\n" );
document.write( "They are\r\n" );
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document.write( "1x24\r\n" );
document.write( "2x12\r\n" );
document.write( "3x8\r\n" );
document.write( "4x6\r\n" );
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document.write( "Now since the last sign before the 8 is +, out to the\r\n" );
document.write( "right of those we ADD those pairs of positive integers:\r\n" );
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document.write( "1x24   1+24=25\r\n" );
document.write( "2x12   2+12=14\r\n" );
document.write( "3x8     3+8=11\r\n" );
document.write( "4x6     6+4=10\r\n" );
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document.write( "Ignoring signs we see that 14 is the coefficient of the\r\n" );
document.write( "middle term, and that corresponds to factors 2 and 12,\r\n" );
document.write( "So we must put signs, either + or -, in front of 2z and 12z \r\n" );
document.write( "so they will combine to give the middle term, +14z.  We \r\n" );
document.write( "can do that by assigning a positive sign to 2z and a \r\n" );
document.write( "positive sign to 12z.  So the middle term +14z can be\r\n" );
document.write( "written as +2z+12z\r\n" );
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document.write( "So\r\n" );
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document.write( "becomes\r\n" );
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document.write( "Factor only the first two terms:\r\n" );
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document.write( "Factor the last two terms:\r\n" );
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document.write( "Now notice there is a common binomial factor of\r\n" );
document.write( ", so we can factor it out:\r\n" );
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document.write( "That's it!\r\n" );
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document.write( "Edwin

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