document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=840292>Question 840292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need some help! Can anyone help me?\r<BR>\n" );
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document.write( "Use the given zero to find the remaining zeros of the function\r<BR>\n" );
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document.write( "h(x)=3x^4+7x^3+69x^2+175x-150; zero:-5i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #506118 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=506118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that if -5i is a zero of the polynomial, then 5i must also be a zero.  If we rewrite these two zeros in factor form, we would have\r<BR>\n" );
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document.write( "(x + 5i)(x - 5i)\r<BR>\n" );
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document.write( "Now, let's expand that, by using the FOIL method.  This will give us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we have a factor of our original polynomial without the i's.  Now, we can use polynomial long division to divide our original function by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+25 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Doing this will give us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B7x-6 ALIGN=MIDDLE  ALT=\"3x%5E2%2B7x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, we can factor this polynomial.  This will give us, in factored form:\r<BR>\n" );
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document.write( "(3x - 2)(x + 3)\r<BR>\n" );
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document.write( "Setting each of these factors equal to zero, will give us our our other two zeroes:\r<BR>\n" );
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document.write( "3x - 2 = 0 -------> 3x = 2 -----> x = 2/3\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "x + 3 = 0 -----> x = -3\r<BR>\n" );
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document.write( "Since the highest degree of our original polynomial function is 4, and we now have found 4 zeroes, we are done.\r<BR>\n" );
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document.write( "Zereos:  -5i, 5i, 2/3, -3 </SPAN>\n" );
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