document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=89097>Question 89097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely. <BR>\n" );
document.write( "      x^2 + 3x – 28<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 #64757 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=64757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-28 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the multiplier of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is 1, the factors of this polynomial must be<BR>\n" );
document.write( "(presuming it factors) one of the following pairs of factors of 28:<BR>\n" );
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document.write( "(28 and 1)<BR>\n" );
document.write( "(14 and 2)<BR>\n" );
document.write( "(7 and 4)<BR>\n" );
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document.write( "Since 28 is preceded by a minus sign, in each factor pair, one of the numbers must be positive<BR>\n" );
document.write( "and the other must be negative.  If they both were positive or they both were negative,<BR>\n" );
document.write( "they would multiply together to give +28.<BR>\n" );
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document.write( "Now look at the middle term in the polynomial ... the one that contains the \"x\". It is <BR>\n" );
document.write( "multiplied by +3.  Therefore, our factor pair must combine to give us +3.<BR>\n" );
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document.write( "There is no way that 28 and 1 can be added or subtracted to give +3.  There is also no<BR>\n" );
document.write( "way that 14 and 2 can be added or subtracted to give +3.  But what about 7 and 4?<BR>\n" );
document.write( "We already know that one of these two numbers must be positive and the other negative.<BR>\n" );
document.write( "How about if the 7 were positive and the 4 were negative. If they were added the result<BR>\n" );
document.write( "would be the +3 we are looking for.  Therefore, we have figured out that +7 and -4 are what<BR>\n" );
document.write( "we need. They multiply to give the -28 and they add to give the +3.<BR>\n" );
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document.write( "We can now form the factored answer of:<BR>\n" );
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document.write( "(x + 7)*(x - 4)<BR>\n" );
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document.write( "Check by multiplying:<BR>\n" );
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document.write( "x*x = x^2<BR>\n" );
document.write( "x*(-4) = -4x<BR>\n" );
document.write( "7*x = +7x<BR>\n" );
document.write( "7*(-4) = -28<BR>\n" );
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document.write( "Combine these four products:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4x+%2B+7x+-+28 ALIGN=MIDDLE  ALT=\"x%5E2+-+4x+%2B+7x+-+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The two terms that contain \"x\" combine to be +3x so the answer becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+-+28 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+-+28\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "And since this is the polynomial that you were asked to factor, the two factors we found<BR>\n" );
document.write( "are correct ... (x + 7)*(x - 4)<BR>\n" );
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document.write( "Hope this helps you to see how you can develop the answer.<BR>\n" );
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