document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=634771>Question 634771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im having trouble factoring polynomials:\r<BR>\n" );
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document.write( "please show the steps and explain (simply) what changes were made and why they were made between steps:\r<BR>\n" );
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document.write( "a few examples of what i am having trouble with:\r<BR>\n" );
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document.write( "(2x^3) + (3x^2) - 8x - 12 = 0\r<BR>\n" );
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document.write( "(x/(x+2) + (1/4) = 5\r<BR>\n" );
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document.write( "x^(5/4) - 32 = 0\r<BR>\n" );
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document.write( "(6x^4) - (23x^2) + 20 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #399882 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=399882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (2x^3) + (3x^2) - 8x - 12 = 0<BR>\n" );
document.write( "factor by grouping<BR>\n" );
document.write( "(2x^3 - 8x)+ (3x^2 - 12) = 0<BR>\n" );
document.write( "2x(x^2-4)+3(x^2-4)=0<BR>\n" );
document.write( "factor out common term<BR>\n" );
document.write( "(x^2-4)(2x+3)=0<BR>\n" );
document.write( "solve for x<BR>\n" );
document.write( "x^2-4=0<BR>\n" );
document.write( "x^2=4<BR>\n" );
document.write( "x=±&#8730;4=±2<BR>\n" );
document.write( "or<BR>\n" );
document.write( "2x+3=0<BR>\n" );
document.write( "2x=-3<BR>\n" );
document.write( "x=-3/2<BR>\n" );
document.write( "x=-2, -3/2, 2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(x/(x+2) + (1/4) = 5<BR>\n" );
document.write( "add(-1/4) to each side<BR>\n" );
document.write( "(x/(x+2) = 20/4-1/4=19/4<BR>\n" );
document.write( "(x/(x+2)=19/4<BR>\n" );
document.write( "cross-multiply<BR>\n" );
document.write( "4x=19(x+2)=19x+38<BR>\n" );
document.write( "15x=-38<BR>\n" );
document.write( "x=-38/15<BR>\n" );
document.write( "x&#8776;2.5333..<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^(5/4) - 32 = 0 <BR>\n" );
document.write( "x^(5/4) = 32<BR>\n" );
document.write( "raise both sides to the 4/5 power<BR>\n" );
document.write( "x=32^(4/5)=16 (take fifth root of 32=2, then raise it to the 4th power=2^4=16<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(6x^4) - (23x^2) + 20 = 0<BR>\n" );
document.write( "6x^4-23x^2+20 = 0<BR>\n" );
document.write( "let u=x^2<BR>\n" );
document.write( "u^2=x^4<BR>\n" );
document.write( "equation:<BR>\n" );
document.write( "6u^2-23u+20=0<BR>\n" );
document.write( "solve for u, using following quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=6, b=-23, c=20<BR>\n" );
document.write( "ans: <BR>\n" );
document.write( "u=2.5<BR>\n" );
document.write( "or<BR>\n" );
document.write( "u=4/3<BR>\n" );
document.write( "solve for x:<BR>\n" );
document.write( "x^2=u=2.5<BR>\n" );
document.write( "x=±&#8730;2.5<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x^2=4/3<BR>\n" );
document.write( "x=±&#8730;(4/3)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x=-&#8730;(4/3), -&#8730;(2.5), &#8730;2.5, and &#8730;(4/3) </SPAN>\n" );
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