document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7756>Question 7756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify all the rational zeros for f(x)=x3(cubed)+4x2(squared)-3x-18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4271 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the zeros of: \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%5E3+%2B+4x%5E2+-+3x+-18 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E3+%2B+4x%5E2+-+3x+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Try factor by grouping:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%5E3+-+8%29+%2B+%284x%5E2+-+3x+-+10%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%5E3+-+8%29+%2B+%284x%5E2+-+3x+-+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the first set of parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+8 ALIGN=MIDDLE  ALT=\"x%5E3+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a difference of two cubes and can be factored as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5E3+-+B%5E3%29+=+%28A+-+B%29%28A%5E2+%2B+AB+%2B+B%5E2%29 ALIGN=MIDDLE  ALT=\"%28A%5E3+-+B%5E3%29+=+%28A+-+B%29%28A%5E2+%2B+AB+%2B+B%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: A = x and B = 2, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+-+8%29+=+%28x+-+2%29%28x%5E2+%2B+2x+%2B+4%29 ALIGN=MIDDLE  ALT=\"%28x%5E3+-+8%29+=+%28x+-+2%29%28x%5E2+%2B+2x+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the second set of parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+3x+-+10 ALIGN=MIDDLE  ALT=\"4x%5E2+-+3x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+3x+-+10+=+%284x+%2B+5%29%28x+-+2%29 ALIGN=MIDDLE  ALT=\"4x%5E2+-+3x+-+10+=+%284x+%2B+5%29%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So, altogether we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+4x%5E2+-+3x+-+18+=+%28x+-+2%29%28x%5E2+%2B+2x++%2B+4%29+%2B+%284x+%2B+5%29%28x+-+2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now, factor out (x - 2):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x+-+2%29%28x%5E2+%2B+2x+%2B+4+%2B+4x+%2B+5%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x+-+2%29%28x%5E2+%2B+2x+%2B+4+%2B+4x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying the 2nd parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x+-+2%29%28x%5E2+%2B+6x+%2B+9%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x+-+2%29%28x%5E2+%2B+6x+%2B+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor the 2nd parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x+-+2%29%28x+%2B+3%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x+-+2%29%28x+%2B+3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now, set this equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29%28x+%2B+3%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+2%29%28x+%2B+3%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and apply the zero product principle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2+=+0 ALIGN=MIDDLE  ALT=\"x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So, the three zeros are:\r<BR>\n" );
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document.write( "x = 2, or x = -3 (a double root)\r<BR>\n" );
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document.write( "Take a look at the graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E3%2B4x%5E2-3x-18%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-5%2C5%2C-10%2C10%2Cx%5E3%2B4x%5E2-3x-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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