document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018703>Question 1018703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When f(x)= ax^2+bx-4 is divided by x+2, the remainder is -2. When f(x) is divided by x+3, the remainder is 5. Find the values of a and b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634755 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=634755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first part means that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-2%29=-2 ALIGN=MIDDLE  ALT=\"f%28-2%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The second part means that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=5 ALIGN=MIDDLE  ALT=\"f%28-3%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The question's solution is based on use of the Remainder and Factor Theorems.  You do not actually need to perform the divisions because the factor & remainder theorems tell you that those results are expected to work; so just solve a system of two equations in two unknowns, being unknowns a and b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Review how the Remainder & Factor Theorems work.<BR>\n" );
document.write( "Substitute the needed values for x to get this system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%2A%28-2%29%5E2%2Bb%2A%28-2%29-4=-2%2Ca%2A%28-3%29%5E2%2Bb%2A%28-3%29-4=5%29 ALIGN=MIDDLE  ALT=\"system%28a%2A%28-2%29%5E2%2Bb%2A%28-2%29-4=-2%2Ca%2A%28-3%29%5E2%2Bb%2A%28-3%29-4=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify the system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284a-2b=2%2C9a-3b=9%29 ALIGN=MIDDLE  ALT=\"system%284a-2b=2%2C9a-3b=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for a and b.  The steps for this are not included here.<BR>\n" );
document.write( "----You must already know how to correctly solve such a system as expected according your course level being COLLEGE ALGEBRA.<BR>\n" );
document.write( "The function you should find is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28f%28x%29=2x%5E2%2B3x-4%29 ALIGN=MIDDLE  ALT=\"highlight%28f%28x%29=2x%5E2%2B3x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );