document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090850>Question 1090850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me please?<BR>\n" );
document.write( "The polynomial function r(x) at right is of at least possible degree and has zeroes at -4,-2,0 and 2, and also passes through the point (-1,3). Find the equation for r(x) in factored form.(I could not draw the graph here...)<BR>\n" );
document.write( "Thank you.<BR>\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 #705302 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13367)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>A polynomial with four zeros has degree 4 or greater.  Since you are looking for the polynomial of least possible degree that has the four give zeros, you want a polynomial of degree exactly 4.  Since it has zeros -4, -2, 0, and 2, it will be of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+a%28x%2B4%29%28x%2B2%29%28x%29%28x-2%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+a%28x%2B4%29%28x%2B2%29%28x%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The constant a will determine how \"steep\" or \"flat\" the graph of the function is.  In particular, it will determine the exact value of the function for any given x value.<br><BR>\n" );
document.write( "So substitute the given x value, -1, into the polynomial and determine the value of a that will produce the given y value, 3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+a%28-1%2B4%29%28-1%2B2%29%28-1%29%28-1-2%29 ALIGN=MIDDLE  ALT=\"3+=+a%28-1%2B4%29%28-1%2B2%29%28-1%29%28-1-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When you have finished solving that equation to determine the value of a, you can write the complete polynomial function.<br><br><BR>\n" );
document.write( "In response to your message...<br><BR>\n" );
document.write( "Yes, a is 1/3; and yes, that is factored form. So the polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+%281%2F3%29%28x%2B4%29%28x%2B2%29%28x%29%28x-2%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+%281%2F3%29%28x%2B4%29%28x%2B2%29%28x%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When I graph that polynomial on my graphing calculator, it has zeros at -4, -2, 0, and 2; and it passes through (-1,3).<br><BR>\n" );
document.write( "Do you have a picture of what the graph is supposed to look like and it looks different?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );