document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959556>Question 959556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7x^3-62x^2+167x-102, 4-i is a zero<BR>\n" );
document.write( "a, find all the zeros<BR>\n" );
document.write( "b,factor f(x)as a product of linear factors<BR>\n" );
document.write( "c,solve the equation f(x)=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586526 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a. find all the zeros\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=7x%5E3-62x%5E2%2B167x-102 ALIGN=MIDDLE  ALT=\"f%28x%29=7x%5E3-62x%5E2%2B167x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-i+ ALIGN=MIDDLE  ALT=\"4-i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is a zero, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bi ALIGN=MIDDLE  ALT=\"4%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a zero\r<BR>\n" );
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document.write( "using zero product formula we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%284-i%29%29%28x-%284%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28x-%284-i%29%29%28x-%284%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B17 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we need to use long division and divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E3-62x%5E2%2B167x-102 ALIGN=MIDDLE  ALT=\"7x%5E3-62x%5E2%2B167x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B17 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-6 ALIGN=MIDDLE  ALT=\"7x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B17 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E3-62x%5E2%2B167x-102+ ALIGN=MIDDLE  ALT=\"7x%5E3-62x%5E2%2B167x-102+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E3-56x%5E2%2B119x ALIGN=MIDDLE  ALT=\"7x%5E3-56x%5E2%2B119x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%5E2%2B48x-102 ALIGN=MIDDLE  ALT=\"-6x%5E2%2B48x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%5E2%2B48x-102 ALIGN=MIDDLE  ALT=\"-6x%5E2%2B48x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------.............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>reminder<BR>\n" );
document.write( "so, third zero is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-6 ALIGN=MIDDLE  ALT=\"7x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the product of all zeros is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287x-6%29%28x-%284-i%29%29%28x-%284%2Bi%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287x-6%29%28x-%284-i%29%29%28x-%284%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287x-6%29+%28x%5E2-8x%2B17%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287x-6%29+%28x%5E2-8x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "b. factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a product of linear factors\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=7x%5E3-62x%5E2%2B167x-102 ALIGN=MIDDLE  ALT=\"f%28x%29=7x%5E3-62x%5E2%2B167x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" >...write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-62x%5E2 ALIGN=MIDDLE  ALT=\"-62x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-56x%5E2-6x%5E2 ALIGN=MIDDLE  ALT=\"-56x%5E2-6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=167x ALIGN=MIDDLE  ALT=\"167x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=119x%2B48x ALIGN=MIDDLE  ALT=\"119x%2B48x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=7x%5E3-56x%5E2-6x%5E2%2B119x%2B48x-102 ALIGN=MIDDLE  ALT=\"f%28x%29=7x%5E3-56x%5E2-6x%5E2%2B119x%2B48x-102\"   DISABLED_style= \"max-width:90%; height:auto;\" >......group<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287x%5E3-6x%5E2%29-%2856x%5E2-48x%29%2B%28119x-102%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287x%5E3-6x%5E2%29-%2856x%5E2-48x%29%2B%28119x-102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%287x-6%29-8x%287x-6%29%2B17%287x-6%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%287x-6%29-8x%287x-6%29%2B17%287x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%287x-6%29%28x%5E2-8x%2B17%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%287x-6%29%28x%5E2-8x%2B17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "c. solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-6%29%28x%5E2-8x%2B17%29=0 ALIGN=MIDDLE  ALT=\"%287x-6%29%28x%5E2-8x%2B17%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or like we have in a.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%2B17%29=%28x-%284-i%29%29%28x-%284%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%2B17%29=%28x-%284-i%29%29%28x-%284%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-6%29%28x-%284-i%29%29%28x-%284%2Bi%29%29=0 ALIGN=MIDDLE  ALT=\"%287x-6%29%28x-%284-i%29%29%28x-%284%2Bi%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x-6%29=0 ALIGN=MIDDLE  ALT=\"%287x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=6 ALIGN=MIDDLE  ALT=\"7x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2F7 ALIGN=MIDDLE  ALT=\"x=6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and two already given zeros<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-i%29 ALIGN=MIDDLE  ALT=\"%284-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Bi%29 ALIGN=MIDDLE  ALT=\"%284%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );