document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123010>Question 123010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I neeed help asap please.\r<BR>\n" );
document.write( "\n" );
document.write( "Use Synthetic division to find the 3 zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B7x%5E2%2B2x-40=0 ALIGN=MIDDLE  ALT=\"x%5E3%2B7x%5E2%2B2x-40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90266 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=90266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Any rational zero can be found through this equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Roots=\frac{p}{q}\"> where p and q are the factors of the last and first coefficients\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's list the factors of -40 (the last coefficient):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p=\pm1, \pm2, \pm4, \pm5, \pm8, \pm10, \pm20, \pm40\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's list the factors of 1 (the first coefficient):\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE q=\pm1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's divide each factor of the last coefficient by each factor of the first coefficient\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{1}, \frac{2}{1}, \frac{4}{1}, \frac{5}{1}, \frac{8}{1}, \frac{10}{1}, \frac{20}{1}, \frac{40}{1}, \frac{-1}{1}, \frac{-2}{1}, \frac{-4}{1}, \frac{-5}{1}, \frac{-8}{1}, \frac{-10}{1}, \frac{-20}{1}, \frac{-40}{1}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These are all the distinct rational zeros of the function that could occur\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  1, 2, 4, 5, 8, 10, 20, 40, -1, -2, -4, -5, -8, -10, -20, -40\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To save time, I'm only going to use synthetic division on the possible zeros that are actually zeros of the function.<BR>\n" );
document.write( "Otherwise, I would have to use synthetic division on every possible root (there are 16 possible roots, so that means there would be at most 16 synthetic division tables).<BR>\n" );
document.write( "However, you might be required to follow this procedure, so this is why I'm showing you how to set up a problem like this\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When you graph this polynomial, you will see that <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;\" > is a zero. So we'll use this for the synthetic division  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now set up the synthetic division table by placing the zero in the upper left corner and placing the coefficients of the polynomial to the right of the test zero.<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply 2 by 1 and place the product (which is 2)  right underneath the second  coefficient (which is 7)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD ></TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add 2 and 7 to get 9. Place the sum right underneath 2.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >9</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply 2 by 9 and place the product (which is 18)  right underneath the third  coefficient (which is 2)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD >18</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >9</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add 18 and 2 to get 20. Place the sum right underneath 18.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD >18</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >9</TD><TD >20</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply 2 by 20 and place the product (which is 40)  right underneath the fourth  coefficient (which is -40)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD >18</TD><TD >40</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >9</TD><TD >20</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add 40 and -40 to get 0. Place the sum right underneath 40.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >2</TD><TD >|</TD><TD >1</TD><TD >7</TD><TD >2</TD><TD >-40</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >2</TD><TD >18</TD><TD >40</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >9</TD><TD >20</TD><TD >0</TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "Since the last column adds to zero, we have a remainder of zero. This means <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;\" > is a factor of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+7x%5E2+%2B+2x+-+40 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+7x%5E2+%2B+2x+-+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets look at the bottom row of coefficients:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first 3 coefficients (1,9,20) form the quotient\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+9x+%2B+20 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+9x+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+%2B+7x%5E2+%2B+2x+-+40%29%2F%28x-2%29=x%5E2+%2B+9x+%2B+20 ALIGN=MIDDLE  ALT=\"%28x%5E3+%2B+7x%5E2+%2B+2x+-+40%29%2F%28x-2%29=x%5E2+%2B+9x+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can use this <a  rel=nofollow HREF=http://calc101.com/webMathematica/long-divide.jsp>online polynomial division calculator</a> to check your work\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Basically  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+7x%5E2+%2B+2x+-+40 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+7x%5E2+%2B+2x+-+40\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%5E2+%2B+9x+%2B+20%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%5E2+%2B+9x+%2B+20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now lets break  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+9x+%2B+20 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+9x+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > down further\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9x%2B20 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 1 and 20 respectively.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now multiply the first coefficient 1 and the last coefficient 20 to get 20. Now what two numbers multiply to 20 and add to the  middle coefficient 9? Let's list all of the factors of 20:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factors of 20:\r<BR>\n" );
document.write( "\n" );
document.write( "1,2,4,5,10,20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These factors pair up and multiply to 20\r<BR>\n" );
document.write( "\n" );
document.write( "1*20\r<BR>\n" );
document.write( "\n" );
document.write( "2*10\r<BR>\n" );
document.write( "\n" );
document.write( "4*5\r<BR>\n" );
document.write( "\n" );
document.write( "(-1)*(-20)\r<BR>\n" );
document.write( "\n" );
document.write( "(-2)*(-10)\r<BR>\n" );
document.write( "\n" );
document.write( "(-4)*(-5)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note: remember two negative numbers multiplied together make a positive number\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  border=\"1\">\n" );
document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">20</TD><TD >1+20=21</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">10</TD><TD >2+10=12</TD></tr><tr><TD  align=\"center\">4</TD><TD  align=\"center\">5</TD><TD >4+5=9</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-20</TD><TD >-1+(-20)=-21</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">-10</TD><TD >-2+(-10)=-12</TD></tr><tr><TD  align=\"center\">-4</TD><TD  align=\"center\">-5</TD><TD >-4+(-5)=-9</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From this list we can see that 4 and 5 add up to 9 and multiply to 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B9x%2B20 ALIGN=MIDDLE  ALT=\"1x%5E2%2B9x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x ALIGN=MIDDLE  ALT=\"9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5x ALIGN=MIDDLE  ALT=\"4x%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B5x ALIGN=MIDDLE  ALT=\"4x%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x ALIGN=MIDDLE  ALT=\"9x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x ALIGN=MIDDLE  ALT=\"9x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bhighlight%284x%2B5x%29%2B20 ALIGN=MIDDLE  ALT=\"x%5E2%2Bhighlight%284x%2B5x%29%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B4x%2B5x%2B20 ALIGN=MIDDLE  ALT=\"1x%5E2%2B4x%2B5x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%29%2B%285x%2B20%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%29%2B%285x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B4%29%2B5%28x%2B4%29 ALIGN=MIDDLE  ALT=\"x%28x%2B4%29%2B5%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group. Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we have a common term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B9x%2B20 ALIGN=MIDDLE  ALT=\"x%5E2%2B9x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B5%29%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B5%29%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now reintroduce the factor <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now set each factor equal to zero:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=0 ALIGN=MIDDLE  ALT=\"x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4=0 ALIGN=MIDDLE  ALT=\"x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now solve for x for each factor:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B7x%5E2%2B2x-40 ALIGN=MIDDLE  ALT=\"x%5E3%2B7x%5E2%2B2x-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5 ALIGN=MIDDLE  ALT=\"x=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );