document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596729>Question 596729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!<BR>\n" );
document.write( "I have a homework that says:<BR>\n" );
document.write( "solve the following quadratic equations by factoring. \r<BR>\n" );
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document.write( "a) x^2+8x+7=0  I tried to solve it and I got this answer (x+1) (x+7)=0.\r<BR>\n" );
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document.write( "b) 2y^2 + 12y +10=0  I got: 2(y^2+6y+5)=0\r<BR>\n" );
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document.write( "c) x^2=81  I'm not sure how o solve this one.\r<BR>\n" );
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document.write( " However the =0 confuses me do I have to use the quadratic formula to solve them?<BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377994 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=377994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would not use the quadratic formula unless I really had to, and the instructions say to use factoring.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B7=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > You factored the quadratic polynomial to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29+%28x%2B7%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29+%28x%2B7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For the product to be zero, one factor must be zero.<BR>\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;\" > gives you one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7=0 ALIGN=MIDDLE  ALT=\"x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you the other solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-7%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%5E2+%2B+12y+%2B10=0 ALIGN=MIDDLE  ALT=\"2y%5E2+%2B+12y+%2B10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > You factored the quadratic polynomial to get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28y%5E2%2B6y%2B5%29=0 ALIGN=MIDDLE  ALT=\"2%28y%5E2%2B6y%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring a little further, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28y%2B1%29%28y%2B5%29=0 ALIGN=MIDDLE  ALT=\"2%28y%2B1%29%28y%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One of those factors must be zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B1=0 ALIGN=MIDDLE  ALT=\"y%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-1%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B5=0 ALIGN=MIDDLE  ALT=\"y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives you the other solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=81 ALIGN=MIDDLE  ALT=\"x%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > is easy, except for the question of using factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=81 ALIGN=MIDDLE  ALT=\"x%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that x is a number that squared equals 81.<BR>\n" );
document.write( "You know one such number: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2=81 ALIGN=MIDDLE  ALT=\"9%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=9%29 ALIGN=MIDDLE  ALT=\"highlight%28x=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one solution.<BR>\n" );
document.write( "There is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-9%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%29%5E2=81 ALIGN=MIDDLE  ALT=\"%28-9%29%5E2=81\"   DISABLED_style= \"max-width:90%; height:auto;\" > too.<BR>\n" );
document.write( "Maybe you were expected to transform it by subtracting 81 from both sides to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-81=0 ALIGN=MIDDLE  ALT=\"x%5E2-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then factor to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-9%29%28x%2B9%29=0 ALIGN=MIDDLE  ALT=\"%28x-9%29%28x%2B9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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