document.write( "Question 991813: find the difference quotient of
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Algebra.Com's Answer #611567 by Edwin McCravy(20056) $\"\"$ $\"About$

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find the difference quotient of
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document.write( "The difference quotient is\r\n" );
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document.write( "First find f(x+h) by substituting (x+h) \r\n" );
document.write( "for each x in \r\n" );
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document.write( "  f(x) = 2x² - 5x + 3 \r\n" );
document.write( "f(x+h) = 2(x+h)² - 5(x+h) + 3\r\n" );
document.write( "f(x+h) = 2(x+h)(x+h) - 5(x+h) + 3\r\n" );
document.write( "f(x+h) = 2(x²+hx+hx+h²) - 5x - 5h + 3\r\n" );
document.write( "f(x+h) = 2(x²+2hx+h²) - 5x - 5h + 3\r\n" );
document.write( "f(x+h) = 2x² + 4hx + 2h² - 5x - 5h + 3\r\n" );
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document.write( "No we substitute that for the f(x+h) in\r\n" );
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document.write( "and we have:\r\n" );
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document.write( "and we substitute (2x² - 5x + 3) for f(x), making sure\r\n" );
document.write( "that we place it inside parentheses, so as not to get\r\n" );
document.write( "any signs wrong since it is preceded by a - sign:\r\n" );
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document.write( "Now we remove the parentheses by changing the signs inside:\r\n" );
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document.write( "We find that all terms in the numerator which do not\r\n" );
document.write( "contain the factor h will cancel and we are left with:\r\n" );
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document.write( "That will allow us to factor out an h in the numerator:\r\n" );
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document.write( "Then we can cancel the h's\r\n" );
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document.write( "And we are left with:\r\n" );
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document.write( "Edwin

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