document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231124>Question 231124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am a mom trying to recall my high school math to help my son. I am having trouble factoring these problems:\r<BR>\n" );
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document.write( "12x(squared) -8x-15\r<BR>\n" );
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document.write( "x(cubed)-125\r<BR>\n" );
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document.write( "8x(cubed)+1\r<BR>\n" );
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document.write( "25x(squared)+36\r<BR>\n" );
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document.write( "Help!! and thanx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171090 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 12x(squared) -8x-15<BR>\n" );
document.write( "Classroom problems almost always have integer factors.  Look for a combination of coefficients that give the -8x.<BR>\n" );
document.write( "12 can be 1*12, 2*6 or 3*4.  15 is 3*5. Since it's -15, the signs will be different.<BR>\n" );
document.write( "Some people use a \"tree\", but that's just listing all possibilities.  Trial and error is quicker, imo.<BR>\n" );
document.write( "12 and 1 don't look likely, I'll try 2 and 6.<BR>\n" );
document.write( "(2x - 3)*(6x + 5)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "x(cubed)-125<BR>\n" );
document.write( "All differences of 2 cubes have the same form:<BR>\n" );
document.write( "a^3 - b^3 = (a-b)*(a^2 + ab + b^2)<BR>\n" );
document.write( "--> (x-5)*(x^2 + 5x + 25)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "8x(cubed)+1<BR>\n" );
document.write( "All sums of 2 cubes have the same form, also:<BR>\n" );
document.write( "a^3 = b^3 = (a+b)*(a^2 - ab + b^2)<BR>\n" );
document.write( "For this one, a is 2x<BR>\n" );
document.write( "(2x)^3 + 1 = (2x+1)*(4x^2 - 2x + 1)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "25x(squared)+36 <BR>\n" );
document.write( "This cannot be factored.  The difference can, but not the sum of 2 squares.  The sum of odd powers can be factored, but not the even powers.<BR>\n" );
document.write( "email me at gsihoutx@aol.com if you have questions. </SPAN>\n" );
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