document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149491>Question 149491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the polynomial below completely, given the bionomial folowing it is a factor of thepoynomial   x^3-4x^2+x+6,   x+1\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109670 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=109670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's simplify this expression using synthetic division\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Start with the given expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+-+4x%5E2+%2B+x+%2B+6%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%5E3+-+4x%5E2+%2B+x+%2B+6%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First lets find our test 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%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so our test zero is -1\r<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 test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.<TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</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 >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</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 -1 by 1 and place the product (which is -1)  right underneath the second  coefficient (which is -4)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</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 -1 and -4 to get -5. Place the sum right underneath -1.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD ></TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >-5</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply -1 by -5 and place the product (which is 5)  right underneath the third  coefficient (which is 1)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >5</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >-5</TD><TD ></TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add 5 and 1 to get 6. Place the sum right underneath 5.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >5</TD><TD ></TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >-5</TD><TD >6</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Multiply -1 by 6 and place the product (which is -6)  right underneath the fourth  coefficient (which is 6)\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >5</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >-5</TD><TD >6</TD><TD ></TD></TR>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "\n" );
document.write( "    Add -6 and 6 to get 0. Place the sum right underneath -6.\r<BR>\n" );
document.write( "\n" );
document.write( "    <TABLE  cellpadding=10>\n" );
document.write( "<TR><TD >-1</TD><TD >|</TD><TD >1</TD><TD >-4</TD><TD >1</TD><TD >6</TD></TR><TR><TD ></TD><TD >|</TD><TD ></TD><TD >-1</TD><TD >5</TD><TD >-6</TD><TD ></TD></TR><TR><TD ></TD><TD ></TD><TD >1</TD><TD >-5</TD><TD >6</TD><TD >0</TD></TR>\n" );
document.write( "</TABLE>\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,-5,6) 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+-+5x+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+%2B+6\"   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+-+4x%5E2+%2B+x+%2B+6%29%2F%28x%2B1%29=x%5E2+-+5x+%2B+6 ALIGN=MIDDLE  ALT=\"%28x%5E3+-+4x%5E2+%2B+x+%2B+6%29%2F%28x%2B1%29=x%5E2+-+5x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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+-+4x%5E2+%2B+x+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E3+-+4x%5E2+%2B+x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%5E2+-+5x+%2B+6%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%5E2+-+5x+%2B+6%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+-+5x+%2B+6 ALIGN=MIDDLE  ALT=\"x%5E2+-+5x+%2B+6\"   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( "\n" );
document.write( "Looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B6 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that the first coefficient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the second coefficient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now multiply the first coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the last term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%286%29=6 ALIGN=MIDDLE  ALT=\"%281%29%286%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now the question is: what two whole numbers multiply to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the previous product) <font size=4><b>and</b></font> add to the second coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find these two numbers, we need to list <font size=4><b>all</b></font> of the factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the previous product).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "1,2,3,6\r<BR>\n" );
document.write( "\n" );
document.write( "-1,-2,-3,-6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These factors pair up and multiply to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "1*6<BR>\n" );
document.write( "2*3<BR>\n" );
document.write( "(-1)*(-6)<BR>\n" );
document.write( "(-2)*(-3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "<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\"><font color=black>1</font></TD><TD   align=\"center\"><font color=black>6</font></TD><TD   align=\"center\"><font color=black>1+6=7</font></TD></tr><tr><TD   align=\"center\"><font color=black>2</font></TD><TD   align=\"center\"><font color=black>3</font></TD><TD   align=\"center\"><font color=black>2+3=5</font></TD></tr><tr><TD   align=\"center\"><font color=black>-1</font></TD><TD   align=\"center\"><font color=black>-6</font></TD><TD   align=\"center\"><font color=black>-1+(-6)=-7</font></TD></tr><tr><TD   align=\"center\"><font color=red>-2</font></TD><TD   align=\"center\"><font color=red>-3</font></TD><TD   align=\"center\"><font color=red>-2+(-3)=-5</font></TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From the table, we can see that the two numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the middle coefficient).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the two numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > both multiply to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <font size=4><b>and</b></font> add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now replace the middle term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x ALIGN=MIDDLE  ALT=\"-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-3x ALIGN=MIDDLE  ALT=\"-2x-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-3x=-5x ALIGN=MIDDLE  ALT=\"-2x-3x=-5x\"   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=x%5E2%2Bhighlight%28-2x-3x%29%2B6 ALIGN=MIDDLE  ALT=\"x%5E2%2Bhighlight%28-2x-3x%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace the second term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x ALIGN=MIDDLE  ALT=\"-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-3x ALIGN=MIDDLE  ALT=\"-2x-3x\"   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%5E2-2x%29%2B%28-3x%2B6%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%29%2B%28-3x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the terms into two pairs.\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-2%29%2B%28-3x%2B6%29 ALIGN=MIDDLE  ALT=\"x%28x-2%29%2B%28-3x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the first 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=x%28x-2%29-3%28x-2%29 ALIGN=MIDDLE  ALT=\"x%28x-2%29-3%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\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-3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Or factor out the common term <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( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B6 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x-2%29\"   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%2B1%29%28x%5E2+-+5x+%2B+6%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%5E2+-+5x+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > now becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------\r<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( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-4x%5E2%2Bx%2B6 ALIGN=MIDDLE  ALT=\"x%5E3-4x%5E2%2Bx%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x-3%29%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x-3%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );