document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=892214>Question 892214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I factor<BR>\n" );
document.write( "3x^2+5x+2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #540363 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=540363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is in the form of ax^2 + bx + c = 0<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = 5<BR>\n" );
document.write( "c = 2<BR>\n" );
document.write( "your factors will be (a1x + c1) * (a2x + c2)<BR>\n" );
document.write( "a1 and a2 are factors of 3, so they will be 3 * 1 or 1 * 3<BR>\n" );
document.write( "c1 and c2 are factors of 2, so they will be 2 * 1 or 1 * 2<BR>\n" );
document.write( "the middle term needs to be a combination of a1*c2 + a2*c1<BR>\n" );
document.write( "since the b term is 5, then a1*c2 * a2*c1 needs to be equal to 5.<BR>\n" );
document.write( "since 5 = 3 + 2, than a1c2 needs to be equal to 2 and a2c1 needs to be equal to 3<BR>\n" );
document.write( "your possible combinations are 3*2 + 1*1 or 3*1 + 1*2<BR>\n" );
document.write( "of these possible combinations, 3*1 + 1*2 looks the most promising.<BR>\n" );
document.write( "so let a1 = 3 and c2 = 1 and let a2 = 1 and c1 = 2 and your factors of (a1x + c1) * (a2x + c2) become (3*x + 2) * (x + 1)<BR>\n" );
document.write( "if you multiply these factors together, you will get 3x^2 + 3x + 2x + 2 which will be equal to 3x^2 + 5x + 2 after you combine like terms.<BR>\n" );
document.write( "your factors are (3x+2)*(x+1)\r<BR>\n" );
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document.write( "there are several different methods you can choose.<BR>\n" );
document.write( "another method is to split the middle term as follows:<BR>\n" );
document.write( "your equation is 3x^2 + 5x + 2<BR>\n" );
document.write( "multiply the coefficiennt of the x^2 term by the constant term to get 3*2 = 6<BR>\n" );
document.write( "now look for all possible factors of 6 until you find a set of factors that will add up to 5.<BR>\n" );
document.write( "1*6 = 6 but doesn't add up to 5<BR>\n" );
document.write( "2*3 = 6 and does add up to 5.<BR>\n" );
document.write( "thoe are your factors.<BR>\n" );
document.write( "now split the middle term into 2x and 3x because they add up to 5xc.<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "3x^2 + 2x + 3x + 2<BR>\n" );
document.write( "now associate the first 2 terms together and the last 2 terms together to get:<BR>\n" );
document.write( "(3x^2 + 2x) + (3x + 2)<BR>\n" );
document.write( "now factor the left term and the right term as much as you can.<BR>\n" );
document.write( "if your left term is left with a factor of 3x+2, you want to get your right term to have a factor of 3x+2 as well.<BR>\n" );
document.write( "it should happen naturally, as it does in this case.<BR>\n" );
document.write( "you will get x*(3x+2) + 1*(3x+2)<BR>\n" );
document.write( "since you have a common factor of (3x+2), you can factor it out to get:<BR>\n" );
document.write( "(x+1)*(3x+2)\r<BR>\n" );
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document.write( "there is another method called the box method which is similar to this last method but uses a box and is a little more formal in the step as hey are carried out.\r<BR>\n" );
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document.write( "all of these methods can be seen online.\r<BR>\n" );
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document.write( "some good references for you to look at are shown below:\r<BR>\n" );
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document.write( "the method of last resort is the quadratic formula.\r<BR>\n" );
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document.write( "if you can't factor the equation any other way, you can always factor it using the quadratic formula.\r<BR>\n" );
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document.write( "that's one of the references below as well.\r<BR>\n" );
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document.write( "there are more, including a new  method i just learned about that i already forgot and the indian method which is an offshoot of the methods referenced below.\r<BR>\n" );
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document.write( "for practical purposes, if you learn the box method and the quadratic formula, you should be in good shape.\r<BR>\n" );
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document.write( "the splitting the b term method i showed you is an offshoot of the box method but a little less formal and a little harder to understand because of the factoring out of the common terms isn't as formalized as in the box method.\r<BR>\n" );
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