document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209682>Question 1209682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2.  Find the remainder when f(x) is divided by x. </SPAN>\n" );
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document.write( "Answer: <font color=red>4</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "Think of \"divided by x\" as \"divided by x-0\"<BR>\n" );
document.write( "Comparing x-0 with x-k shows k = 0\r<BR>\n" );
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document.write( "Remainder Theorem: <BR>\n" );
document.write( "When dividing p(x) over (x-k), the remainder is p(k)\r<BR>\n" );
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document.write( "This means we go with f(0) = <font color=red>4</font>\r<BR>\n" );
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document.write( "A slightly more in-depth look:<BR>\n" );
document.write( "f(x)/g(x) = quotient + remainder/g(x)<BR>\n" );
document.write( "f(x) = g(x)*quotient + remainder<BR>\n" );
document.write( "f(x) = x*quotient + remainder<BR>\n" );
document.write( "f(0) = 0*quotient + remainder<BR>\n" );
document.write( "f(0) = remainder = <font color=red>4</font><BR>\n" );
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