document.write( "Question 1208160: \"cross%28Is%29\"If x^2 + 5x + 7 is prime, show the \"cross%28prove%29\"proof. \n" ); document.write( "
Algebra.Com's Answer #846366 by Plocharczyk(17)\"\" \"About 
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document.write( "x2 + 5x + 7\r\n" );
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document.write( "In order to determine whether the quadratic is prime or not, we need to decide\r\n" );
document.write( "if it can be factorized. Any quadratic is prime if it cannot be factorized. The\r\n" );
document.write( "quadratic in this example, x2 + 5x + 7, has a leading coefficient, or\r\n" );
document.write( "coefficient of x2, equal to 1.\r\n" );
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document.write( "This means that it is a case of simple factorization, where we need to find two\r\n" );
document.write( "numbers with a product of +7 and a sum of +5. The sum of the two numbers needs\r\n" );
document.write( "to be the coefficient of x. And the product of the two numbers needs to be equal\r\n" );
document.write( "to the free term. The only product of two integers that equals 7 is 1 and 7, as\r\n" );
document.write( "1 multiplied by 7 is equal to 7.\r\n" );
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document.write( "However, these numbers do not have a sum of 5, as 1 plus 7 is equal to 8, not 5.\r\n" );
document.write( "As there is no pair of numbers with a product of +7 and a sum of +5, we can say\r\n" );
document.write( "that the quadratic x2 + 5x + 7 is prime and therefore cannot be factorized.\r\n" );
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document.write( "Edwin
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