document.write( "Question 1034208: 1. A polynomial function is shown below.
\n" ); document.write( " f(x) = x^6 + 12x^5 + 43x^4 + 22x^3
\n" ); document.write( " a. Find the real zeros of f (x).
\n" ); document.write( " b. Express f (x) in terms of linear factors.
\n" ); document.write( " c. Find all of the zeros of f (x).
\n" ); document.write( " (3 points)
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Algebra.Com's Answer #648808 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( " 1. A polynomial function is shown below.
\n" ); document.write( " f(x) = x^6 + 12x^5 + 43x^4 + 22x^3
\n" ); document.write( " a. Find the real zeros of f (x).
\n" ); document.write( " b. Express f (x) in terms of linear factors.
\n" ); document.write( " c. Find all of the zeros of f (x).
\n" ); document.write( " (3 points)
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document.write( "First, factor by taking x^3 out:\r\n" );
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document.write( "f(x) =   = .\r\n" );
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document.write( "Next, check that x = -1 is the root of the polynomial in parentheses  .\r\n" );
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document.write( "So, the polynomial in parentheses has the factor (x+1).\r\n" );
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document.write( "Make long division and factor this polynomial:\r\n" );
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document.write( " = .\r\n" );
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document.write( "The quadratic polynomial  x^2 + 11x + 32  has no real roots (since its discriminant  = -7 is negative).\r\n" );
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document.write( "Thus you can not factor this quadratic polynomial further over real domain.\r\n" );
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document.write( "Therefore, your final factoring over the real domain is \r\n" );
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document.write( "f(x) =  = .\r\n" );
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document.write( "The two real roots are x = 0  and x = -1.\r\n" );
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document.write( "The complex zeroes of the polynomial x^2 + 11x + 32 are \r\n" );
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document.write( " =   and   = .\r\n" );
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