document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22569>Question 22569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My homework is on factoring trinommials and i dont understand it. one problem i have is (the 2 after the b is squared like i dont know how to square it on here): b2+20b+36=0 and i dont know what to do. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11015 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=11015\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factoring trinomials. <BR>\n" );
document.write( "N.B. You can indicate a square by using the caret (^), thus...x^2 = x-squared.<BR>\n" );
document.write( "Example, factor:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+20b+%2B+36+=+0 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+20b+%2B+36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "When you factor a trinomial such as the one above, you are looking for two binomials that will look like this: (b + m)(b + n) and when you multiply these binomial factors, you will get back the trinomial you started with.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+20b+%2B+36+=+%28b+%2B+m%29%28b+%2B+n%29 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+20b+%2B+36+=+%28b+%2B+m%29%28b+%2B+n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So, what are m and n and how do you find them?\r<BR>\n" );
document.write( "\n" );
document.write( "Let's multiply the two binomials (b + m)(b + n) and compare the result with the original trinomial.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+m%29%28b+%2B+n%29+=+b%5E2+%2B+nb+%2B+mb+%2B+mn%29 ALIGN=MIDDLE  ALT=\"%28b+%2B+m%29%28b+%2B+n%29+=+b%5E2+%2B+nb+%2B+mb+%2B+mn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+%28m%2Bn%29b+%2B+mn ALIGN=MIDDLE  ALT=\"b%5E2+%2B+%28m%2Bn%29b+%2B+mn\"   DISABLED_style= \"max-width:90%; height:auto;\" > compare this with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+%2B+20b+%2B+36 ALIGN=MIDDLE  ALT=\"b%5E2+%2B+20b+%2B+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "You can see that for these two trinomials to be equal, then (m+n) = 20 and mn = 36. That is, you are looking for two integers whose sum is 20 and whose product is 36. Let's try some examples:\r<BR>\n" );
document.write( "\n" );
document.write( "4 X 9 = 36 and 4 + 9 = 13  No good!<BR>\n" );
document.write( "6 X 6 = 36 and 6 + 6 = 12  No good!<BR>\n" );
document.write( "2 X 18 = 36 and 2 + 18 = 20 Bingo! So, m = 2 and n = 18\r<BR>\n" );
document.write( "\n" );
document.write( "So, mn = 2(18) = 36 and m+n = 2+18 = 20\r<BR>\n" );
document.write( "\n" );
document.write( "Now you can write your two binomial factors (b + m)(b + n) as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+2%29%28b+%2B+18%29+=+b%5E2+%2B+20b+%2B+36 ALIGN=MIDDLE  ALT=\"%28b+%2B+2%29%28b+%2B+18%29+=+b%5E2+%2B+20b+%2B+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );