document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=480903>Question 480903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5x^4 - 45x^3 + 25x^2<BR>\n" );
document.write( "What is the complete factorization? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329380 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=329380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E4+-45x%5E3+%2B+25x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E4+-45x%5E3+%2B+25x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2 ALIGN=MIDDLE  ALT=\"5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-common factor for all three terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%28x%5E2+-9x+%2B+5%29 ALIGN=MIDDLE  ALT=\"5x%5E2%28x%5E2+-9x+%2B+5%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=5x%5E2%28x%5E2+-9x+%2B+5%29 ALIGN=MIDDLE  ALT=\"5x%5E2%28x%5E2+-9x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >..now try to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-9x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2+-9x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=factoring_quadratics.solver>Factoring Quadratics with a leading coefficient of 1 (a=1)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>In order to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%5E2%2B-9%2Ax%2B5 ALIGN=MIDDLE  ALT=\"1%2Ax%5E2%2B-9%2Ax%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, first we need to ask ourselves: What two numbers multiply to 5 and add to -9? Lets find out by listing all of the possible factors of 5<BR>\n" );
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document.write( "  Factors:<BR>\n" );
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document.write( "  1,5,<BR>\n" );
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document.write( "  -1,-5,List the negative factors as well. This will allow us to find all possible combinations<BR>\n" );
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document.write( "  These factors pair up to multiply to 5.<BR>\n" );
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document.write( "  1*5=5<BR>\n" );
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document.write( "  (-1)*(-5)=5<BR>\n" );
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document.write( "  note: remember two negative numbers multiplied together make a positive number<BR>\n" );
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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<BR>\n" );
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document.write( "  <TABLE><TR><TD>First Number</TD><TD >|</TD><TD >Second Number</TD><TD >|</TD><TD >Sum</TD></TR><TR><TD >1</TD><TD >|</TD><TD >5</TD>|</TD><TD >|</TD><TD >1+5=6</TD></TR><TR><TD >-1</TD><TD >|</TD><TD >-5</TD>|</TD><TD >|</TD><TD >-1+(-5)=-6</TD></TR><TABLE>\r\n" );
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document.write( "  None of these factors add to -9. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.</TD></TR>\n" );
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document.write( "as you can see, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-9x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2+-9x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be factored; so, your solution is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%28x%5E2+-9x+%2B+5%29 ALIGN=MIDDLE  ALT=\"5x%5E2%28x%5E2+-9x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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