document.write( "Question 457765: Please help me ...Find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1. \n" ); document.write( "

Algebra.Com's Answer #314027 by Edwin McCravy(20060) $\"\"$ $\"About$

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Please help me ...Find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1.
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document.write( "Start by listing \"x = ↏\" as many times as the multiplicity\r\n" );
document.write( "of each zero, for every zero:\r\n" );
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document.write( "x = -2,  x = -2, x = 0, x = 3\r\n" );
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document.write( "[Notice that I listed x = -2 twice because it has \r\n" );
document.write( "multiplicity 2]\r\n" );
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document.write( "Get 0 on the right of each of those equations:\r\n" );
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document.write( "x + 2 = 0, x + 2 = 0, x = 0, x - 3 = 0\r\n" );
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document.write( "[Notice that x = 0 already had a 0 on the right side]\r\n" );
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document.write( "Now indicate the multiplication of the left sides\r\n" );
document.write( "of all of those equations and set it = 0\r\n" );
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document.write( "(x + 2)(x + 2)(x)(x - 3) = 0\r\n" );
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document.write( "Now multiply that out.\r\n" );
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document.write( "Multiplying the first two factors:\r\n" );
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document.write( "(x² + 4x + 4)(x)(x - 3) = 0\r\n" );
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document.write( "Multiply the first two factor of this:\r\n" );
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document.write( "(x³ + 4x² + 4x)(x - 3) = 0\r\n" );
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document.write( "Multiply those:\r\n" );
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document.write( "x⁴- 3x³ + 4x³ - 12x² + 4x² - 12x = 0\r\n" );
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document.write( "Collect like terms:\r\n" );
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document.write( "x⁴+ x³ - 8x² - 12x = 0\r\n" );
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document.write( "The polynomial itself does not contain the = 0\r\n" );
document.write( "on the end, so the answer is just the left side:\r\n" );
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document.write( "P(x) = x⁴+ x³ - 8x² - 12x\r\n" );
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document.write( "Edwin

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