document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765440>Question 765440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all zeros of the following polynomial. Write the polynomial in factored form.\r<BR>\n" );
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document.write( "f(x) = 4x^3 + 7x^2 + 6x - 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466150 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=466150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+4x%5E3+%2B+7x%5E2+%2B+6x+-+2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+4x%5E3+%2B+7x%5E2+%2B+6x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >..writ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2 ALIGN=MIDDLE  ALT=\"7x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-x%5E2 ALIGN=MIDDLE  ALT=\"8x%5E2-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x-2x ALIGN=MIDDLE  ALT=\"8x-2x\"   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=f%28x%29+=+4x%5E3%2B8x%5E2%2B8x-x%5E2-2x-2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+4x%5E3%2B8x%5E2%2B8x-x%5E2-2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%284x%5E3-x%5E2%29%2B%288x%5E2-2x%29%2B%288x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%284x%5E3-x%5E2%29%2B%288x%5E2-2x%29%2B%288x-2%29\"   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=f%28x%29+=+x%5E2%284x-1%29%2B2x%284x-1%29%2B2%284x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2%284x-1%29%2B2x%284x-1%29%2B2%284x-1%29\"   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=f%28x%29+=+%284x-1%29%28x%5E2%2B2x%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%284x-1%29%28x%5E2%2B2x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x-1%29%28x%5E2%2B2x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284x-1%29%28x%5E2%2B2x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-1=0 ALIGN=MIDDLE  ALT=\"4x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=1 ALIGN=MIDDLE  ALT=\"4x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F4 ALIGN=MIDDLE  ALT=\"x=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now use quadratic formula to find remaining two roots from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B2x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2B2%29=0\"   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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   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=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+\"   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=x+=+%28-2+%2B-+sqrt%28+4-8+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4-8+%29%29%2F2+\"   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=x+=+%28-2+%2B-+sqrt%28+-4+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+-4+%29%29%2F2+\"   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=x+=+%28-2+%2B-+2i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+2i%29%2F2+\"   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=x+=+-2%2F2+%2B-+2i%2F2+ ALIGN=MIDDLE  ALT=\"x+=+-2%2F2+%2B-+2i%2F2+\"   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=x+=+-1+%2B-+i+ ALIGN=MIDDLE  ALT=\"x+=+-1+%2B-+i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1+%2B+i+ ALIGN=MIDDLE  ALT=\"x+=+-1+%2B+i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1+-+i+ ALIGN=MIDDLE  ALT=\"x+=+-1+-+i+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have one real and two complex roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C600%2C+-10%2C10%2C+-10%2C+10%2C+4x%5E3+%2B+7x%5E2+%2B+6x+-+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C600%2C+-10%2C10%2C+-10%2C+10%2C+4x%5E3+%2B+7x%5E2+%2B+6x+-+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );