document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209693>Question 1209693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the remainder when the polynomial<BR>\n" );
document.write( "g(x) = x^3 - 14x^2 - 67x - 90 + 5x^3 - 20x^2 + 7x - 135<BR>\n" );
document.write( "is divided by x - 1?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849825 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the remainder when g(x) is divided by x - 1, we can use the Remainder Theorem. The Remainder Theorem states that if we divide a polynomial g(x) by (x - c), the remainder is g(c). In this case, we are dividing by x - 1, so c = 1.\r<BR>\n" );
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document.write( "First, let's simplify g(x) by combining like terms:<BR>\n" );
document.write( "g(x) = (x^3 + 5x^3) + (-14x^2 - 20x^2) + (-67x + 7x) + (-90 - 135)<BR>\n" );
document.write( "g(x) = 6x^3 - 34x^2 - 60x - 225\r<BR>\n" );
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document.write( "Now, we need to find g(1):<BR>\n" );
document.write( "g(1) = 6(1)^3 - 34(1)^2 - 60(1) - 225<BR>\n" );
document.write( "g(1) = 6 - 34 - 60 - 225<BR>\n" );
document.write( "g(1) = -313\r<BR>\n" );
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document.write( "Therefore, the remainder when g(x) is divided by x - 1 is -313.\r<BR>\n" );
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document.write( "Final Answer: The final answer is $\boxed{-313}$<BR>\n" );
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