document.write( "Question 1200924: Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)\r
\n" ); document.write( "\n" ); document.write( "P(x) = 2x^3 + 7x^2 + 4x − 4\r
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\n" ); document.write( "\n" ); document.write( "Write the polynomial in factored form.\r
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Algebra.Com's Answer #835155 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
\n" ); document.write( "P(x) = 2x^3 + 7x^2 + 4x − 4
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\n" ); document.write( "Write the polynomial in factored form.
\n" ); document.write( "P(x) =
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document.write( "According to Rational Zeroes theorem, the list of possible rational zeroes consists of these values\r\n" );
document.write( "{1, -1, 2, -2, 4, -4}.\r\n" );
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document.write( "It is easy to check that x= -2 is the root.\r\n" );
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document.write( "Then the given polynomial is divisible by (x+2), so we divide the given polynomial\r\n" );
document.write( "by (x+2) to reduce the degree\r\n" );
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document.write( "     = 2x^2 + 3x - 2.\r\n" );
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document.write( "Regarding quadratic polynomial  2x^2 + 3x - 2, we can factor it by grouping\r\n" );
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document.write( "    2x^2 + 3x - 2 = (2x^2 + 4x) - (x+2) = 2x*(x+2) - (x+2) = (2x-1)*(x+2).\r\n" );
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document.write( "Therefore, the final decomposition of the given polynomial is \r\n" );
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document.write( "    2x^3 + 7x^2 + 4x − 4 = .\r\n" );
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document.write( "It has the roots x= -2 of multiplicity 2 and x= 1/2 of multiplicity 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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