document.write( "Question 1051320: Use the given zero to find the remaining zeros of the polynomial function. (Enter your answers as a comma-separated list.)
\n" ); document.write( "P(x) = x^3 + 11x^2 + x + 11; -i \n" ); document.write( "

Algebra.Com's Answer #666848 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "The first thing you need is that complex zeros always appear in conjugate pairs. So write the given zero in complex number,

form:

. The conjugate of

, so the companion zero to the one given is

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\n" ); document.write( "\n" ); document.write( "If

is a zero of a polynomial, then

must be a factor of the polynomial. Hence, we now know two of the factors of the given polynomial, to wit:\r
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\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "and\r
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\n" ); document.write( "\n" ); document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "Since this is a binomial conjugate pair, their product is the difference of two squares. Remember that

. Hence:\r
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\r
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\n" ); document.write( "\n" ); document.write( "Use polynomial long division to divide the original polynomial function by

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document.write( "                                   x  +  11\r\n" );
document.write( "              -----------------------------\r\n" );
document.write( "x^2 + 0x + 1  |  x^3  +  11x^2  +  x  +  11\r\n" );
document.write( "                 x^3      0x^2  +  x\r\n" );
document.write( "                 --------------------------\r\n" );
document.write( "                         11x^2  + 0x  +  11\r\n" );
document.write( "                         11x^2  + 0x  +  11\r\n" );
document.write( "                        -------------------\r\n" );
document.write( "                                          0\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "So the third and final factor is

and therefore the third and final zero is -11\r
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\n" ); document.write( "\n" ); document.write( "By the way, saying x2 or x3 to mean x squared or x cubed is confusing. Use the caret mark (^) to indicate raising to a power, such as x^5 or e^x, which we all understand to mean

. If you want more information on rendering mathematical expressions in plain text, review Formatting Math as Text (Note that there are four pages of information).\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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