document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76401>Question 76401</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321143183/algebrahomeworkh>Developmental Mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need to factor the following and provide pairs of factors and sums of factors<BR>\n" );
document.write( "I don't quite get the text book\r<BR>\n" );
document.write( "\n" );
document.write( "X with exponential of 2 +8x+15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54809 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=54809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2B15 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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, you know that the factors must be of the<BR>\n" );
document.write( "form:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x __ ___)*(x __ ___)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice that if you multiply these two leading factors, the result is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax+=+x%5E2 ALIGN=MIDDLE  ALT=\"x%2Ax+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "that we need.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The two underscored blanks in each set of parentheses represent the sign (positive or negative) <BR>\n" );
document.write( "and the number value.  Notice that the two numbers must be factors of 15 so that when they<BR>\n" );
document.write( "are multiplied they produce +15.  Therefore they need to be either 1 and 15 or 3 and 5 <BR>\n" );
document.write( "so that they produce 15. For this problem they must both be positive or both be negative <BR>\n" );
document.write( "so that their product is positive 15. The two numbers must also produce +8 when they are <BR>\n" );
document.write( "added algebraically because +8 is the multiplier of the middle term.  15 and 1 cannot<BR>\n" );
document.write( "produce +8 but 3 and 5 can work.  So let's put them into our factors to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x __ 3)(x __ 5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice again that multiplying the first two terms in each set of parentheses you get x-squared<BR>\n" );
document.write( "and multiplying the last terms in each set of parentheses gives you 15. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Are the signs both plus or both minus?  The 3 and the 5 must add to be + 8 not -8. Therefore,<BR>\n" );
document.write( "the signs in our factors must both be +. So our factors are:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x + 3)(x + 5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you can multiply these two factors together you will find that they result in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+8x+%2B+15 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8x+%2B+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "which checks and verifies that our factors are correct.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope that this supplements what your book says in such a way that it enables you to understand<BR>\n" );
document.write( "the basic process. The process basically involves factoring the first term and then <BR>\n" );
document.write( "factoring the last term.  If the factors of the first term are 1x and 1x then the factors<BR>\n" );
document.write( "of the last terms must be capable of producing the value of the middle term when they are <BR>\n" );
document.write( "added.  You need to watch the sign of the last term and the middle term so that you can<BR>\n" );
document.write( "determine if the factors need to be both +, both - , or one + and one -.  After working a<BR>\n" );
document.write( "few problems such as this one, you will get the hang of it. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );