document.write( "Question 108149: Problem #1\r
\n" ); document.write( "\n" ); document.write( "For the function
\n" ); document.write( " h(x) = x³ - x² - 17x - 15,
\n" ); document.write( "Use long division to determine which of the following are factors of h(x).
\n" ); document.write( "a) x + 5 b) x + 1 c) x + 3\r
\n" ); document.write( "\n" ); document.write( "Problem #2
\n" ); document.write( "Determine the oblique asymptote of the graph of the function.
\n" ); document.write( "
\n" ); document.write( "g(x)= (x² + 4x - 1)/(x + 3)\r
\n" ); document.write( "\n" ); document.write( "Thanks.\r
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Algebra.Com's Answer #78964 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "For the function\r\n" );
document.write( "h(x) = x³ - x² - 17x - 15,\r\n" );
document.write( "Use long division to determine which of the following are factors of h(x).\r\n" );
document.write( "a) x + 5 b) x + 1 c) x + 3 \r\n" );
document.write( "\r\n" );
document.write( "Divide x³ - x² - 17x - 15 by x + 5 to see if (a) is a factor of h(x)\r\n" );
document.write( "\r\n" );
document.write( "            x² -  6x + 13\r\n" );
document.write( "     --------------------\r\n" );
document.write( "x + 5)x³ -  x² - 17x - 15\r\n" );
document.write( "      x² + 5x²\r\n" );
document.write( "      --------\r\n" );
document.write( "         - 6x² - 17x\r\n" );
document.write( "         - 6x² - 30x\r\n" );
document.write( "         -----------\r\n" );
document.write( "                 13x - 15\r\n" );
document.write( "                 13x + 65\r\n" );
document.write( "                 --------\r\n" );
document.write( "                     - 80\r\n" );
document.write( "\r\n" );
document.write( "No, (a) is not a factor because we get a remainder of -80,\r\n" );
document.write( "not 0.\r\n" );
document.write( "\r\n" );
document.write( "So, we divide x3 - x2 - 17x - 15 by x + 1 to see if (b) is a factor\r\n" );
document.write( "of h(x)\r\n" );
document.write( "\r\n" );
document.write( "            x² -  2x - 15\r\n" );
document.write( "     --------------------\r\n" );
document.write( "x + 1)x³ -  x² - 17x - 15\r\n" );
document.write( "      x² +  x²\r\n" );
document.write( "      --------\r\n" );
document.write( "         - 2x² - 17x\r\n" );
document.write( "         - 2x² -  2x\r\n" );
document.write( "         -----------\r\n" );
document.write( "               - 15x - 15\r\n" );
document.write( "               - 13x - 15\r\n" );
document.write( "                 --------\r\n" );
document.write( "                        0\r\n" );
document.write( "\r\n" );
document.write( "Yes, (b) is a factor of h(x) because we get a remainder of 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide x3 - x2 - 17x - 15 by x + 5 to see if (c) is a factor\r\n" );
document.write( "of h(x).\r\n" );
document.write( "\r\n" );
document.write( "            x² -  4x -  5\r\n" );
document.write( "     --------------------\r\n" );
document.write( "x + 3)x³ -  x² - 17x - 15\r\n" );
document.write( "      x² + 3x²\r\n" );
document.write( "      --------\r\n" );
document.write( "         - 4x² - 17x\r\n" );
document.write( "         - 4x² - 12x\r\n" );
document.write( "         -----------\r\n" );
document.write( "               -  5x - 15\r\n" );
document.write( "               -  5x - 15\r\n" );
document.write( "                 --------\r\n" );
document.write( "                        0\r\n" );
document.write( "\r\n" );
document.write( "Yes, (c) is a factor of h(x) because we get a remainder of 0.\r\n" );
document.write( "\r\n" );
document.write( "So (b) and (c) are factors and (a) is not a factor.\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Problem #2\r\n" );
document.write( "Determine the oblique asymptote of the graph of the function.\r\n" );
document.write( "\r\n" );
document.write( "g(x)= (x² + 4x - 1)/(x + 3)\r\n" );
document.write( "\r\n" );
document.write( "We divide the expression on the right using long division:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "            x + 1\r\n" );
document.write( "     ------------\r\n" );
document.write( "x + 3)x² + 4x + 1\r\n" );
document.write( "      x² + 3x\r\n" );
document.write( "      -------\r\n" );
document.write( "            x + 1 \r\n" );
document.write( "            x + 3\r\n" );
document.write( "            -----\r\n" );
document.write( "              - 2\r\n" );
document.write( "\r\n" );
document.write( "Now use h(x) =  =  +   \r\n" );
document.write( "\r\n" );
document.write( "        h(x) = x + 1 + \r\n" );
document.write( "\r\n" );
document.write( "The fraction on the right becomes nearer and nearer to zero as x takes\r\n" );
document.write( "on values with larger and larger absolute values.  So therefore the graph\r\n" );
document.write( "of h(x) becomes nearer and nearer to the graph of the right hand side\r\n" );
document.write( "without the  term, so the oblique (slanted)\r\n" );
document.write( "asymptote has the equation:\r\n" );
document.write( "\r\n" );
document.write( "          y = x + 1 \r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of h(x) and the green line is the oblique asymptote,\r\n" );
document.write( "whose equation is y = x + 1\r\n" );
document.write( "\r\n" );
document.write( "[The blue line is the vertical asymptote, whose equation is x = -3\r\n" );
document.write( "gotten by setting the denominator x+3 equal to 0.]\r\n" );
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document.write( " \r\n" );
document.write( "Edwin

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