document.write( "Question 1207397: The expression x^2 -x -a, where 0 < a < 100 can be factored into (x-p)(x+q), where p,q are positive integers. How many different values of a are there? \n" ); document.write( "
Algebra.Com's Answer #845252 by ikleyn(52782)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "I will re-write the solution by @greenestamps, correcting mistakes there.\r
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\n" ); document.write( "\"%28x-p%29%28x%2Bq%29=x%5E2%2B%28p-q%29x-pq\"

\n" ); document.write( "The requirements are that (1) p and q are positive integers; (2) -p+q = -1, or p = q+1; and (3) pq is less than 100.

\n" ); document.write( "Simple enumeration shows that p can have any integer value from 2 to 10 inclusive. That's 9 values.

\n" ); document.write( "ANSWER: 9
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\n" ); document.write( "\n" ); document.write( "Now everything is correct.\r
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