document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76085>Question 76085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help factor my homework question. thanks! \r<BR>\n" );
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document.write( "(3x+2)(x-3)= 7x-1<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 #54629 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%2A%28x-3%29=+7x-1 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%2A%28x-3%29=+7x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First multiply out the left side of the equation using the FOIL method (multiply First terms,<BR>\n" );
document.write( "then Outside terms, then Inside terms, and then Last terms) and then collect like terms.<BR>\n" );
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document.write( "The FOIL multiplication of the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2Ax%29+%2B+%283x%2A%28-3%29%29+%2B+%282%2Ax%29+%2B+%282%2A%28-3%29%29+=+7x+-1 ALIGN=MIDDLE  ALT=\"%283x%2Ax%29+%2B+%283x%2A%28-3%29%29+%2B+%282%2Ax%29+%2B+%282%2A%28-3%29%29+=+7x+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The multiplications on the left side result in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+9x+%2B+2x+-+6+=+7x+-+1 ALIGN=MIDDLE  ALT=\"3x%5E2+-+9x+%2B+2x+-+6+=+7x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Collect the like terms on the left side and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+7x+-+6+=+7x+-+1 ALIGN=MIDDLE  ALT=\"3x%5E2+-+7x+-+6+=+7x+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 7x from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+14x+-+6+=+-+1 ALIGN=MIDDLE  ALT=\"3x%5E2+-+14x+-+6+=+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally add +1 to both sides and you get the standard form of:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+-+14x+-+5+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+-+14x+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side of this equation can be factored. Since the 3 can only factor to 3*1 and also<BR>\n" );
document.write( "since the -5 can only factor into 5*1 (without knowing whether the 5 or the 1 has the<BR>\n" );
document.write( "minus sign) ... the factors are either:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+_+5%29%2A%28x+_+1%29+=+0 ALIGN=MIDDLE  ALT=\"%283x+_+5%29%2A%28x+_+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+_+1%29%2A%28x+_+5%29+=+0 ALIGN=MIDDLE  ALT=\"%283x+_+1%29%2A%28x+_+5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "with the signs still to be added within each set of parentheses. <BR>\n" );
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document.write( "The middle term of the quadratic polynomial is multiplied by -14.  Therefore the cross products<BR>\n" );
document.write( "must combine to be -14.  Looks like the last group of factors is capable of producing that<BR>\n" );
document.write( "result.  The 3x times -5 would give -15x and the x times +1 would give +x.  And the -15x and<BR>\n" );
document.write( "the +x would combine to give us - 14x.  Therefore we can write the factored equation as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+1%29%2A%28x+-+5%29+=+0 ALIGN=MIDDLE  ALT=\"%283x+%2B+1%29%2A%28x+-+5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that this equation would be true if either of the multiplied factors on the left<BR>\n" );
document.write( "side was equal to zero.<BR>\n" );
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document.write( "One at a time set the two factors equal to zero to find the values of x that will satisfy<BR>\n" );
document.write( "the equation.  <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"3x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- subtract 1 from both sides to eliminate the +1 on the left.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+-1 ALIGN=MIDDLE  ALT=\"3x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- divide both sides by +3, the multiplier of x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F3 ALIGN=MIDDLE  ALT=\"x+=+-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- one value of x that satisfies the equation.<BR>\n" );
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document.write( "Then for the second factor:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+5+=+0 ALIGN=MIDDLE  ALT=\"x+-+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- add 5 to both sides to eliminate the -5 on the left side.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B5 ALIGN=MIDDLE  ALT=\"x+=+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--- the second value of x that satisfies the equation.<BR>\n" );
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document.write( "Hope this gives you a little more insight into factoring in general and also in solving<BR>\n" );
document.write( "a quadratic equation if factoring the polynomial is possible.<BR>\n" );
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