document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389735>Question 389735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x+2 is a factor of x^2+bx+10, what is the value of b?<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 #276275 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, by inspection, we see that the other factor has to be (x+5) because there's no other factor that will give us 10 as the third term<BR>\n" );
document.write( "(x+2)(x+5)=x^2+7x+10; therefore b=7\r<BR>\n" );
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document.write( "Here's another way:<BR>\n" );
document.write( "Let x+a be the other factor, so:<BR>\n" );
document.write( "(x+2)(x+a)=x^2+bx+10<BR>\n" );
document.write( "Expand the left side using FOIL (First, Outer, Inner, Last)<BR>\n" );
document.write( "x^2+ax+2x+2a=x^2+bx+10 simplifying<BR>\n" );
document.write( "x^2+(a+2)x+2a=x^2+bx+10<BR>\n" );
document.write( "Now we know that the left side is identical to the right side.  That means that the two expressions are identical term for term, so:\r<BR>\n" );
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document.write( "1=1<BR>\n" );
document.write( "a+2=b<BR>\n" );
document.write( "2a=10 or a=5<BR>\n" );
document.write( "a+2=b or 5+2=b; so b=7\r<BR>\n" );
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document.write( "Hope this helps-----ptaylor\r<BR>\n" );
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