document.write( "Question 49054: Factor \"21y%5E4%2B49y%5E3%2B14y%5E2\" \n" ); document.write( "
Algebra.Com's Answer #32507 by AnlytcPhil(1806)\"\" \"About 
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Factor\r\n" );
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document.write( "21y4 + 49y3 +14y2\r\n" );
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document.write( "First we look for a number to take out,\r\n" );
document.write( "which is 7, because 7 is the largest integer\r\n" );
document.write( "that is a factor of 21, 49 and 14\r\n" );
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document.write( "Now we look for a letter.  The smallest power of\r\n" );
document.write( "y that occurs in every term is y².\r\n" );
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document.write( "So we factor out 7y²\r\n" );
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document.write( "7y²(3y² + 7y + 2)\r\n" );
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document.write( "7y²(3y² + 7y + 2)\r\n" );
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document.write( "Multiply the red 3 by the blue 2, which gives\r\n" );
document.write( "6, Now since the green sign is \" + \", we \r\n" );
document.write( "think of two integers which have product equal\r\n" );
document.write( "to 6 and which have sum equal to the purple 7.\r\n" );
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document.write( "Such integers are 6 and 1. So we use these to\r\n" );
document.write( "rewrite the 7y as 6y + 1y\r\n" );
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document.write( "7y²(3y² + 6y + 1y + 2)\r\n" );
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document.write( "We change the parentheses to brackets so we\r\n" );
document.write( "can put parentheses inside them:\r\n" );
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document.write( "7y²[3y² + 6y + 1y + 2]\r\n" );
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document.write( "Now we factor 3y out of the first two terms\r\n" );
document.write( "in the brackets\r\n" );
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document.write( "7y²[3y(y + 2) + 1y + 2]\r\n" );
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document.write( "Now we factor 1 out of the last two terms in\r\n" );
document.write( "the brackets:\r\n" );
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document.write( "7y²[3y(y + 2) + 1(y + 2)]\r\n" );
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document.write( "Now notice that inside the brackets there is\r\n" );
document.write( "a common factor of (y + 2)\r\n" );
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document.write( "So within the bracets take out the common\r\n" );
document.write( "factor (y + 2) and put the factors 3y and +1\r\n" );
document.write( "inside parentheses on the right:\r\n" );
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document.write( "7y²[(y + 2)(3y + 1)]\r\n" );
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document.write( "Now we can erase the brackets and get\r\n" );
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document.write( "7y²(y + 2)(3y + 1)\r\n" );
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document.write( "Edwin
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