document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=36976>Question 36976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5x^4-12x^3=0\r<BR>\n" );
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document.write( "these exponents are blowing my mind. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #22736 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=22736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Think of exponents in the simplest way possible. Forget x, y, z, etc.<BR>\n" );
document.write( "2 is a simple number (1 is really too simple for this)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2+=+2%5E4 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2+=+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "count up the # of 2's - that's the exponent<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2%2A2%2A2%2A2+=+2%5E7 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2%2A2%2A2%2A2+=+2%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now multiply<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2+=+2%5E11 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2%2A2+=+2%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you just add the exponents<BR>\n" );
document.write( "It's a lot easier to write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+%2A+2%5E7+=+2%5E11 ALIGN=MIDDLE  ALT=\"2%5E4+%2A+2%5E7+=+2%5E11\"   DISABLED_style= \"max-width:90%; height:auto;\" > than all those 2's<BR>\n" );
document.write( "That's the point of exponents- it's EASIER<BR>\n" );
document.write( "but you have to acquire rules<BR>\n" );
document.write( "like how do you add? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7+%2B+2%5E4 ALIGN=MIDDLE  ALT=\"2%5E7+%2B+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "not obvious<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E7+%2B+2%5E4+=+2%5E4%2A%282%5E3+%2B+1%29 ALIGN=MIDDLE  ALT=\"2%5E7+%2B+2%5E4+=+2%5E4%2A%282%5E3+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "do it the long way, too<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A2%2A2%2A2%2A2%2A2+%2B+2%2A2%2A2%2A2+=+2%2A2%2A2%2A2+%2A+%282%2A2%2A2+%2B+1%29 ALIGN=MIDDLE  ALT=\"2%2A2%2A2%2A2%2A2%2A2%2A2+%2B+2%2A2%2A2%2A2+=+2%2A2%2A2%2A2+%2A+%282%2A2%2A2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I just factored out 2*2*2*2<BR>\n" );
document.write( "go back and forth<BR>\n" );
document.write( "easy way - hard way<BR>\n" );
document.write( "easy way - hard way<BR>\n" );
document.write( "If you play with it enough and show yourself what's true and <BR>\n" );
document.write( "what isn't- you'll have no trouble with the x's, y's, and z's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax%5E4+-+12%2Ax%5E3+=+0 ALIGN=MIDDLE  ALT=\"5%2Ax%5E4+-+12%2Ax%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2A+%285%2Ax+-+12%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+%2A+%285%2Ax+-+12%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I factored out x^3<BR>\n" );
document.write( "what makes this true?<BR>\n" );
document.write( "If x is zero, I get<BR>\n" );
document.write( "0 times something = 0<BR>\n" );
document.write( "that's certainly true<BR>\n" );
document.write( "Inside the parenthesis, if x= 12/5, then<BR>\n" );
document.write( "12/5*(12/5 - 12/5) = 0<BR>\n" );
document.write( "that's certainly true, also<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "x = 12/5<BR>\n" );
document.write( "are the solutions<BR>\n" );
document.write( "  </SPAN>\n" );
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