document.write( "Question 1123541: Let f(m) = m˄5 - 11m˄3 - 26m˄2 + 48m + 144. Given that m = -2 + 2i and m = -2 are
\n" ); document.write( "roots of f(m), find all the other roots of f(m) and write f(m) as a product of irreducible real quadratic and linear functions. \n" ); document.write( "

Algebra.Com's Answer #739869 by josgarithmetic(39617) $\"\"$ $\"About$

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\n" ); document.write( "Let f(m) = m˄5 - 11m˄3 - 26m˄2 + 48m + 144. Given that -2 + 2i and -2 are
\n" ); document.write( "roots of f(m), find all the other roots of f(m) and write f(m) as a product of irreducible real quadratic and linear functions.
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\n" ); document.write( "\n" ); document.write( "Your given complex root AND its conjugate, together will give you a quadratic root or factor of f(m), $\"m%5E2%2B4m%2B8\"$ . Divide f(m) by $\"m%5E2%2B4m%2B8\"$ ; and then work the rest of the function's factoring...\r
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\n" ); document.write( "\n" ); document.write( "I'm not showing that process, but $\"m%5E5%2B0m%5E4-11m%5E3-26m%5E2%2B48m%2B144\"$ DIVIDED BY $\"m%5E2%2B4m%2B8\"$ is $\"m%5E3-4m%5E2-8m%2B18\"$ . Now, use synthetic division to \"test for \" root $\"-2\"$ , and work with the resulting quotient of that.\r
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\n" ); document.write( "\n" ); document.write( "You're given root of $\"-2\"$ for the factor $\"x%2B2\"$ .
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document.write( "-2   |   1   -4  -3     18\r\n" );
document.write( "     |\r\n" );
document.write( "     |      -2   12    -18\r\n" );
document.write( "     |______________________\r\n" );
document.write( "        1   -6    9      0\r\n" );
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document.write( "This meaning, the resulting factor to continue being  .\r\n" );
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Recognize that this is a perfect square trinomial, $\"%28m-3%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"highlight%28f%28m%29=%28x%2B2%29%28m%5E2%2B4m%2B8%29%28m-3%29%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Complex roots of polynomial functions occur as conjugate pair.
\n" ); document.write( "The given root -2+2i means that -2-2i is also a root of your function. You can get the resulting quadratic factor starting as
\n" ); document.write( " $\"%28m-%28-2%2B2i%29%29%28m-%28-2-2i%29%29\"$ .
\n" ); document.write( "Perform the indicated multiplication of that. Remember as you go, $\"i%5E2=-1\"$ . \n" ); document.write( "

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