document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31921>Question 31921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard time understanding the step by step process in factor competely. Here are my answer, but I'm still not comfortable with it, please check my work and point out my errors. Greatly apprecated.Thank you \r<BR>\n" );
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document.write( "Factor completely:<BR>\n" );
document.write( "x2 – 5x – 14<BR>\n" );
document.write( "x^2-5x-7\r<BR>\n" );
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document.write( "Factor completely:<BR>\n" );
document.write( "4x2 – 36y2<BR>\n" );
document.write( "=2x^2-18y^2<BR>\n" );
document.write( "=(2x^2- 9y^2)<BR>\n" );
document.write( "=(2x^2-3y^2)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18498 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=18498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The goal in factoring trinomials/binomials, as you have in your problem, is to find the two binomials which, when multiplied together, will result in the given trinomial/binomial. Now not all trinomials/binomials are factorable, but in general, you can nearly always find two such binomials. The trick is to use the right technique for your particular trinomial/binomial.\r<BR>\n" );
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document.write( "In the first one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for example, you have have divided the constant term (14) by 2. Why did you do this?\r<BR>\n" );
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document.write( "Here's an approach you might try:<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14\"   DISABLED_style= \"max-width:90%; height:auto;\" > You want to find two binomials of the form<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bm%29%28x-n%29 ALIGN=MIDDLE  ALT=\"%28x%2Bm%29%28x-n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that:<BR>\n" );
document.write( "m X n = -14 and<BR>\n" );
document.write( "m + n = -5\r<BR>\n" );
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document.write( "Using a bit of trial & error:<BR>\n" );
document.write( "2 X (-7) = -14<BR>\n" );
document.write( "(-2) X 7 = -14\r<BR>\n" );
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document.write( "2 + (-7) = -5 This works!<BR>\n" );
document.write( "(-2) + 7 = 5 This doesn't work!\r<BR>\n" );
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document.write( "So from the above, m = 2 and n = -7\r<BR>\n" );
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document.write( "The factors are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x-14+=+%28x%2B2%29%28x-7%29 ALIGN=MIDDLE  ALT=\"x%5E2-5x-14+=+%28x%2B2%29%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For you second problem, notice that your binomial is \"the difference of two squares\". There is a formula for factoring these:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2+-+B%5E2+=+%28A-B%29%28A%2BB%29 ALIGN=MIDDLE  ALT=\"A%5E2+-+B%5E2+=+%28A-B%29%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the A and B in your binomial, you must take the square root of each term.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%284x%5E2%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%284x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+sqrt%2836y%5E2%29 ALIGN=MIDDLE  ALT=\"B+=+sqrt%2836y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6y<BR>\n" );
document.write( "Now substitute these values for A (2x) and B (6y) into the formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-36y%5E2+=+%282x-6y%29%282x%2B6y%29 ALIGN=MIDDLE  ALT=\"4x%5E2-36y%5E2+=+%282x-6y%29%282x%2B6y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this helps! </SPAN>\n" );
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