document.write( "Question 521405: List the possible rational zeros of the function using the rational zero theorem
\n" ); document.write( "g(x)= 9x^5 + 3x^3 + 7x - 4\r
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\n" ); document.write( "g(x)= x^3 + 4x^2 - x - 4 \n" ); document.write( "

Algebra.Com's Answer #346470 by Edwin McCravy(20054) $\"\"$ $\"About$

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List the possible rational zeros of the function using the rational zero theorem
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document.write( "1. Get all possible numerators of rational zeros by listing all the\r\n" );
document.write( "possible divisors of the absolute value of the constant term.\r\n" );
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document.write( "In this case the constant term is -4.  It's absolute cvalue is 4.\r\n" );
document.write( "The divisors of 4 are 1,2, and 4, since they are the only integers\r\n" );
document.write( "which divide evenly into 4.\r\n" );
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document.write( "2. Get all possible denominators of rational zeros by listing all the\r\n" );
document.write( "possible divisors of the coefficient of the largest power of x.\r\n" );
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document.write( "In this case the term with the largest power of x is 9x^5 and the absolute value of its coefficient is 9. The divisors of 9 are 1,3, and 9, since \r\n" );
document.write( "they are the only integers which divide evenly into 4.\r\n" );
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document.write( "3. Make all possible fractions having a numerator from the set of possible\r\n" );
document.write( "numerators and a denominator from the set of possible denominators.\r\n" );
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document.write( "In this case that would be \r\n" );
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document.write( ", , , , , , , ,  \r\n" );
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document.write( "4. Reduce them, and remove any duplications (sometimes there are duplications,\r\n" );
document.write( "there just aren't any here).\r\n" );
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document.write( "1, , , 2, ,, 4, , \r\n" );
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document.write( "5. Give them both signs, + and -\r\n" );
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document.write( "±1, , , ±2, ,, ±4, , \r\n" );
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document.write( "------------------------------------------------\r\n" );
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document.write( "Find all real zeros of the function.\r\n" );
document.write( "g(x)= x^3 + 4x^2 - x - 4\r\n" );
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document.write( "We don't even need the above method to do this \r\n" );
document.write( "one because it can be factored by grouping:\r\n" );
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document.write( "g(x) = x³ + 4x² - x - 4\r\n" );
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document.write( "g(x) = x²(x + 4) - 1(x + 4)\r\n" );
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document.write( "g(x) = (x + 4)(x² - 1)\r\n" );
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document.write( "g(x) = (x + 4)(x - 1)(x + 1)\r\n" );
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document.write( "So the zeros are found by setting all the factors = 0\r\n" );
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document.write( "x + 4 = 0,       x - 1 = 0,      x + 1 = 0\r\n" );
document.write( "    x = -4,          x = 1,          x = -1\r\n" );
document.write( "  \r\n" );
document.write( "Edwin

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