document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209906>Question 209906</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321466204/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 3a^5-24a^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158649 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=158649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No instructions were given but I assume you want to factor.\r<BR>\n" );
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document.write( "Factor out the common factor 3a^2 and then divide each term of the polynomial by the common factor.\r<BR>\n" );
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document.write( "3a^5 divided by 3a^2 = a^3\r<BR>\n" );
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document.write( "-24a^2 divided by 3a^2 = -8\r<BR>\n" );
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document.write( "We now have:\r<BR>\n" );
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document.write( "3a^2(a^3 - 8)\r<BR>\n" );
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document.write( "However, inside the parenthese we have the difference of two perfect cubes.\r<BR>\n" );
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document.write( "We must factor what's inside the parentheses.\r<BR>\n" );
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document.write( "We use the formula to do so:\r<BR>\n" );
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document.write( "a^3 – b^3 = (a – b)(a^2 + ab + b^2) \r<BR>\n" );
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document.write( "Now, a^3 - 8 can be rewritten as a^3 - 2^3.\r<BR>\n" );
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document.write( "NOTE: 8 = 2^3 (in case you're wondering where 2^3 came from).\r<BR>\n" );
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document.write( "We now plug that into the formula and simplify.\r<BR>\n" );
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document.write( "a^3 - 2^3 = (a - 2)(a^2 + 2a + 4)\r<BR>\n" );
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document.write( "Final answer: (3a^2)(a - 2)(a^2 + 2a + 4)\r<BR>\n" );
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