document.write( "Question 1204777: form a polynomial f(x) with real coefficients having the given degree and zeros degree :4, zeros: 5+2i, -1 multiplicity 2 \n" ); document.write( "

Algebra.Com's Answer #841256 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is a very routine exercise. Almost to fitting a formula!\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-%285%2B2i%29%29%28x-%285-2i%29%29%28x%2B1%29%5E2\"$
\n" ); document.write( "Carry through all the multiplication and simplifications....\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-5-2i%29%28x-5%2B2i%29%28x%2B1%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28%28x-5%29-2i%29%28%28x-5%29%2B2i%29%28x%5E2%2B2x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28%28x-5%29%5E2-%282i%29%5E2%29%28x%5E2%2B2x%2B1%29\"$ , recognize what makes Difference Of Two Squares\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-10x%2B25-4i%5E2%29%28x%5E2%2B2x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-10x%2B25-4%28-1%29%29%28x%5E2%2B2x%2B1%29\"$ , understand meaning of i^2\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-10x%2B29%29%28x%5E2%2B2x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Choosing lattice form for the polynomial multiplication
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\r\n" );
document.write( "            x^2        2x        1\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "x^2    |    x^4         2x^3      x^2\r\n" );
document.write( "       |\r\n" );
document.write( "-10x   |   -10x^3      -20x^2     -10x\r\n" );
document.write( "       |\r\n" );
document.write( "29     |  29x^2         58x       29\r\n" );
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\n" ); document.write( "Resulting in $\"highlight%28x%5E4-8x%5E3%2B10x%5E2%2B48x%2B29%29\"$ \n" ); document.write( "

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