document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703877>Question 703877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+x%5E2+%3E=+0 ALIGN=MIDDLE  ALT=\"2x%5E3+-+x%5E2+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2A%282x+-+1%29+%3E=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2A%282x+-+1%29+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and solutions are: x = 0 or x >= 1/2, because:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+1+%3E=+0 ALIGN=MIDDLE  ALT=\"2x+-+1+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+1%2F2 ALIGN=MIDDLE  ALT=\"x+%3E=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%3E=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+sqrt%280%29 ALIGN=MIDDLE  ALT=\"x+%3E=+sqrt%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but why x = 0 and not x >= 0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433768 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=433768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AN PICTURE IS WORD A THOUSAND WORDS:<BR>\n" );
document.write( "This is how my 11th grade math teacher taught me how to solve that kind of problem. (Teachers may have tried to teach me some math earlier than that, but I was not paying too much attention).<BR>\n" );
document.write( "The sign of a product:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C300%2C-2%2C5%2C-1%2C5.2%2C%0D%0Alocate%28-2%2C0.4%2Cx%5E2%282x+-+1%29%29%2Clocate%28-0.5%2C1%2Cnumber_line%28350%2C+-2%2C+3%2C+0%2C+1%2F2%29%29%2C%0D%0Alocate%28-2%2C2.3%2C%282x+-+1%29%29%2Clocate%28-0.5%2C3%2Cnumber_line%28350%2C+-2%2C+3%2C+-5%2C1%2F2%29%29%2C%0D%0Alocate%28-2%2C4.4%2Cx%5E2%29%2Clocate%28-0.5%2C5%2Cnumber_line%28350%2C+-2%2C+3%2C+0%2C-5%29%29%2C%0D%0Alocate%28-0.35%2C1%2C%22-%22%29%2Clocate%280.15%2C1%2C%22-%22%29%2Clocate%280.65%2C1%2C%22-%22%29%2Clocate%281.15%2C1%2C%22-%22%29%2C%0D%0Alocate%281.4%2C0.95%2C0%29%2C%0D%0Alocate%281.65%2C1%2C%22-%22%29%2Clocate%281.9%2C0.95%2C0%29%2Clocate%282.2%2C1%2C%22%2B%22%29%2Clocate%282.7%2C1%2C%22%2B%22%29%2C%0D%0Alocate%283.2%2C1%2C%22%2B%22%29%2Clocate%283.7%2C1%2C%22%2B%22%29%2Clocate%284.2%2C1%2C%22%2B%22%29%2C%0D%0Alocate%28-0.35%2C3%2C%22-%22%29%2Clocate%280.15%2C3%2C%22-%22%29%2Clocate%280.65%2C3%2C%22-%22%29%2Clocate%281.15%2C3%2C%22-%22%29%2C%0D%0Alocate%281.4%2C3%2C%22-%22%29%2C%0D%0Alocate%281.65%2C3%2C%22-%22%29%2Clocate%281.9%2C2.95%2C0%29%2Clocate%282.2%2C3%2C%22%2B%22%29%2Clocate%282.7%2C3%2C%22%2B%22%29%2C%0D%0Alocate%283.2%2C3%2C%22%2B%22%29%2Clocate%283.7%2C3%2C%22%2B%22%29%2Clocate%284.2%2C3%2C%22%2B%22%29%2Clocate%280.2%2C3%2C%22-%22%29%2C%0D%0Alocate%28-0.35%2C5%2C%22%2B%22%29%2Clocate%280.15%2C5%2C%22%2B%22%29%2Clocate%280.65%2C5%2C%22%2B%22%29%2Clocate%281.15%2C5%2C%22%2B%22%29%2C%0D%0Alocate%281.4%2C4.95%2C0%29%2C%0D%0Alocate%281.65%2C5%2C%22%2B%22%29%2Clocate%281.9%2C5%2C%22%2B%22%29%2Clocate%282.2%2C5%2C%22%2B%22%29%2Clocate%282.7%2C5%2C%22%2B%22%29%2C%0D%0Alocate%283.2%2C5%2C%22%2B%22%29%2Clocate%283.7%2C5%2C%22%2B%22%29%2Clocate%284.2%2C5%2C%22%2B%22%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > You place pluses, minuses, and zeros on the stacked (lined up) number lines for each factor.<BR>\n" );
document.write( "Then, you figure out the pluses, minuses, and zeros of the product and write them on  the bottom number line (the one for the product)<BR>\n" );
document.write( " <BR>\n" );
document.write( "GRAPHS:<BR>\n" );
document.write( "<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;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1.5%2C1.5%2C-0.5%2C0.5%2Cx%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1.5%2C1.5%2C-0.5%2C0.5%2Cx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29 ALIGN=MIDDLE  ALT=\"%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-5%2C5%2C2x-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-5%2C5%2C2x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%282x-1%29 ALIGN=MIDDLE  ALT=\"x%5E2%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1.5%2C1.5%2C-0.5%2C0.5%2Cx%5E2%282x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1.5%2C1.5%2C-0.5%2C0.5%2Cx%5E2%282x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "AN EXPLANATION IN MANY WORDS:<BR>\n" );
document.write( "<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;\" > is zero for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For all other values 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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%3E0 ALIGN=MIDDLE  ALT=\"x%5E2%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is positive,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2A%282x+-+1%29+ ALIGN=MIDDLE  ALT=\"x%5E2%2A%282x+-+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > will go along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29 ALIGN=MIDDLE  ALT=\"%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "being negative for all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C1%2F2 ALIGN=MIDDLE  ALT=\"x%3C1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "except for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%3C0 ALIGN=MIDDLE  ALT=\"%282x-1%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "but because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%282x-1%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%282x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At that point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%282x-1%29 ALIGN=MIDDLE  ALT=\"x%5E2%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > refuses to go along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29 ALIGN=MIDDLE  ALT=\"%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );