document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167067>Question 167067</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1932628274/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I don't understand how to get the final answer to this type of problem.\r<BR>\n" );
document.write( "\n" );
document.write( "Fourth degree, zeros of -5,-2,1, and 3, and y-intercept of 15.\r<BR>\n" );
document.write( "\n" );
document.write( "p(x)=a(x+5)(x+2)(x-1)(x-3)<BR>\n" );
document.write( "p(0)=a(5)(2)(-1)(-3)=30a<BR>\n" );
document.write( "30a=15  a=1/2\r<BR>\n" );
document.write( "\n" );
document.write( "p(x)=1/2(x+5)(x+2)(x-1)(x-3) How do you mutiply out the four linear factors and the constant?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123043 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distributive property<BR>\n" );
document.write( "Let's look at Z(C+D)=ZC+ZD.<BR>\n" );
document.write( "What if Z=A+B?<BR>\n" );
document.write( "Then <BR>\n" );
document.write( "Z(C+D)=(A+B)(C+D)=ZC+ZD=(A+B)C+(A+B)D=AC+BC+AD+BD<BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x%2B2%29=x%2Ax%2B5x%2B2x%2B10=x%5E2%2B7x%2B10 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x%2B2%29=x%2Ax%2B5x%2B2x%2B10=x%5E2%2B7x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x-3%29=x%2Ax%2B%28-3%29x%2B%28-1%29x%2B3=x%5E2-4x%2B3 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x-3%29=x%2Ax%2B%28-3%29x%2B%28-1%29x%2B3=x%5E2-4x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the FOIL method for expanding quadratic equations from factors.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now the problem becomes,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=%281%2F2%29%28x%2B5%29%28x%2B2%29%28x-1%29%28x-3%29+=%281%2F2%29%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's look at the product of the two quadratics,<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We again have to use the distributive property and make sure we account for each term. <BR>\n" );
document.write( "There are nine terms in all.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B3%29=%0D%0Ax%5E2%2A%28x%5E2-4x%2B3%29%2B%0D%0A7x%2A%28x%5E2-4x%2B3%29%2B%0D%0A10%2A%28x%5E2-4x%2B3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B3%29=%0D%0Ax%5E2%2A%28x%5E2%29%2Bx%5E2%28-4x%29%2Bx%5E2%283%29%2B%0D%0A7x%2A%28x%5E2%29%2B7x%28-4x%29%2B7x%283%29%2B%0D%0A10%2A%28x%5E2%29%2B10%28-4x%29%2B10%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B10%29=%0D%0Ax%5E4-4x%5E3%2B3x%5E2%2B%0D%0A7x%5E3-28x%5E2%2B21x%2B%0D%0A10x%5E2-40x%2B30 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B10%29=%0D%0Ax%5E4%2B%28-4%2B7%29x%5E3%2B%283-28%2B10%29x%5E2%2B%2821-40%29x%2B30 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B10%29=%0D%0Ax%5E4%2B3x%5E3-15x%5E2-19x%2B30 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B7x%2B10%29%28x%5E2-4x%2B10%29=%0D%0Ax%5E4%2B3x%5E3-15x%5E2-19x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we'll put that back in our original function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=%281%2F2%29%28x%5E4%2B3x%5E3-15x%5E2-19x%2B30%29 ALIGN=MIDDLE  ALT=\"p%28x%29=%281%2F2%29%28x%5E4%2B3x%5E3-15x%5E2-19x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=%281%2F2%29x%5E4%2B%283%2F2%29x%5E3-%2815%2F2%29x%5E2-%2819%2F2%29x%2B15%29 ALIGN=MIDDLE  ALT=\"p%28x%29=%281%2F2%29x%5E4%2B%283%2F2%29x%5E3-%2815%2F2%29x%5E2-%2819%2F2%29x%2B15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check, as an exercise, that we didn't make any mistakes and that x= -5,-2,1, and 3 are in fact zeros of this polynomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%280%29=15 ALIGN=MIDDLE  ALT=\"p%280%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So that checks out.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );