document.write( "Question 473399: I have a factoring issue. I apologize if my question is in the incorrect category.\r
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document.write( "I am given this trinomial to factor: 14m^2+43m+20.\r
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document.write( "I understand how to use the \"AC method\" but do I just sit here and plug numbers into a calculator all day or is there a \"shortcut\" on how to find the two integers whose product is 280 and whose sum is 43? I just don't \"get it\", any help is appreciated.\r
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document.write( "Thanks! \n" );
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Algebra.Com's Answer #324640 by stanbon(75887)![]() ![]() ![]() You can put this solution on YOUR website! 14m^2+43m+20 \n" ); document.write( "---- \n" ); document.write( "Check the discriminant to see \n" ); document.write( "that b^2-4ac = 43^2-4*14*20 = 729 \n" ); document.write( "--- \n" ); document.write( "Since it is greater than zero you have 2 unequal Real roots. \n" ); document.write( "And sqrt(729) = 27 \n" ); document.write( "--- \n" ); document.write( "So you have roots at [-43+-27]/(28) \n" ); document.write( "= -16/28 = -4/7 and -70/28 = -10/4 = -5/2 \n" ); document.write( "--- \n" ); document.write( "So the factors of your quadratic are: \n" ); document.write( "(7x+4)(2x+5) \n" ); document.write( "--- \n" ); document.write( "With the AC Method you were looking for 8 and 35. \n" ); document.write( "--- \n" ); document.write( "How can you shorten the search. \n" ); document.write( "B = 43 tells you the numbers you want are not around 1,280 \n" ); document.write( "sqrt(280) ~ 17 tells you you don't have to look beyond 17 \n" ); document.write( "for the smaller of the 2 numbers. \n" ); document.write( "That might lead you to try 10,28; you fall short of 43 but \n" ); document.write( "you are close. \n" ); document.write( "------ \n" ); document.write( "Another shortcut beside the discriminant is graphing. \n" ); document.write( "Graph the quadratic and y = 0 and see where they intersect. \n" ); document.write( "================= \n" ); document.write( "Cheers, \n" ); document.write( "Stan H. \n" ); document.write( " |