document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78471>Question 78471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to study for a test and I can not figure how to do this question.\r<BR>\n" );
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document.write( "The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2. Find f(3).<BR>\n" );
document.write( "a. -5<BR>\n" );
document.write( "b. -2<BR>\n" );
document.write( "c. 2<BR>\n" );
document.write( "d. 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56276 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=56276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2F%28x-3%29=x%5E2%2B3x-5%2B2%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2F%28x-3%29=x%5E2%2B3x-5%2B2%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"The polynomial f(x) divided x-3 results in a quotient of x^2+3x-5 with a remainder of 2\"\r<BR>\n" );
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document.write( "So multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for f(x)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28x-3%29%28f%28x%29%2Fcross%28x-3%29%29=%28x-3%29%28x%5E2%2B3x-5%2B2%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"cross%28x-3%29%28f%28x%29%2Fcross%28x-3%29%29=%28x-3%29%28x%5E2%2B3x-5%2B2%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-3%29%28x%5E2%2B3x-5%2B2%2F%28x-3%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-3%29%28x%5E2%2B3x-5%2B2%2F%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let y=x-3 to make multiplication easier\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=y%28x%5E2%2B3x-5%2B2%2Fy%29 ALIGN=MIDDLE  ALT=\"f%28x%29=y%28x%5E2%2B3x-5%2B2%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2y%2B3xy-5y%2B2%2Ay%2Fy%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2y%2B3xy-5y%2B2%2Ay%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2y%2B3xy-5y%2B2%2Across%28y%29%2Fcross%28y%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2y%2B3xy-5y%2B2%2Across%28y%29%2Fcross%28y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the y's cancel on the last term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%28x-3%29%2B3x%28x-3%29-5%28x-3%29%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%28x-3%29%2B3x%28x-3%29-5%28x-3%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now replace y with x-3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2Ax-x%5E3%2A3%2B3x%2Ax-3x%2A3-5%2Ax-5%2A3%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2Ax-x%5E3%2A3%2B3x%2Ax-3x%2A3-5%2Ax-5%2A3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-3x%5E2%2B3x%5E2-9x-5x%2B15%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-3x%5E2%2B3x%5E2-9x-5x%2B15%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-14x%2B17 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-14x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "So our function f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-14x%2B17 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-14x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice if we divide f(x) by x-3 we get our original problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2F%28x-3%29=%28x%5E3-14x%2B17%29%2F%28x-3%29=x%5E2%2B3x-5%2B2%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2F%28x-3%29=%28x%5E3-14x%2B17%29%2F%28x-3%29=x%5E2%2B3x-5%2B2%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since we know the function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-14x%2B17 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-14x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" > then f(3) is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29=%283%29%5E3-14%283%29%2B17=27-42%2B17=2 ALIGN=MIDDLE  ALT=\"f%283%29=%283%29%5E3-14%283%29%2B17=27-42%2B17=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So in other words, f(3)=2. So the answer is c) </SPAN>\n" );
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