document.write( "Question 22375: I am to factor 3y^2+10y+7, the trinomial using the ac method. Can someone help me answer this question. \n" ); document.write( "

Algebra.Com's Answer #11642 by AnlytcPhil(1807) $\"\"$ $\"About$

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I am to factor 3y^2+10y+7, the trinomial using the ac method. Can someone\r\n" );
document.write( "help me answer this question.\r\n" );
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document.write( "Step by Step method for factoring a trinomial\r\n" );
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document.write( "Ax² + Bx + C (any letter may be where x is here)\r\n" );
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document.write( "Step 1: If a greatest common factor can be factored out, do\r\n" );
document.write( "that first, then apply the following to the resulting\r\n" );
document.write( "trinomial in parentheses.\r\n" );
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document.write( "Step 2.  Multiply together AC and list the factors of AC.\r\n" );
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document.write( "Step 3.  Find a pair that adds to B.  If you cannot find such\r\n" );
document.write( "a pair then the trinomial does not factor.\r\n" );
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document.write( "Step 4.  Rewrite the middle term as a sum of terms whose\r\n" );
document.write( "coefficients are the chosen pair.\r\n" );
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document.write( "Step 5.  Factor by grouping. \r\n" );
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document.write( "To factor  \r\n" );
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document.write( "        3y² + 10y + 7\r\n" );
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document.write( "AC = (3)(7) = 21\r\n" );
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document.write( "the factor pairs are \r\n" );
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document.write( "        {1,21} and  {3,7}         \r\n" );
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document.write( "We see that  \r\n" );
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document.write( "        3 + 7  =  10   hence we choose the pair {3,7}\r\n" );
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document.write( "We write  \r\n" );
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document.write( "        3y² + 10y + 7\r\n" );
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document.write( "        3y² + 3y + 7y + 7\r\n" );
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document.write( "Then we group the first two terms and the last two terms.\r\n" );
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document.write( "       (3y² + 3y) + (7y + 7)\r\n" );
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document.write( "Factor 3y out of the first parentheses and 7 out of the second.\r\n" );
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document.write( "       3y(y + 1) + 7(y + 1)  \r\n" );
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document.write( "Factor out the common factor (y + 1)\r\n" );
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document.write( "       (y + 1)(3y + 7)\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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