document.write( "Question 205009: I have a homework assignment and I am not sure what to do. What is the Rational Zero Test? List and find zeros of f(x) from function f(x)=x^3+9x^2+8x-60. \n" ); document.write( "
Algebra.Com's Answer #154744 by Edwin McCravy(20060)![]() ![]() You can put this solution on YOUR website! I have a homework assignment and I am not sure what to do. What is the Rational Zero Test? List and find zeros of f(x) from function f(x)=x^3+9x^2+8x-60. \n" ); document.write( " \r\n" ); document.write( "Since the leading coefficient is 1, the possible \r\n" ); document.write( "rational zeros are the integer divisors of the numerical \r\n" ); document.write( "term in absolute value. \r\n" ); document.write( "\r\n" ); document.write( "The possible rational zeros are therefore the factors of 60 \r\n" ); document.write( "and their negatives.\r\n" ); document.write( "\r\n" ); document.write( "±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60 \r\n" ); document.write( "\r\n" ); document.write( "So we start trying. We try 1:\r\n" ); document.write( "\r\n" ); document.write( "x^3+9x^2+8x-60\r\n" ); document.write( "\r\n" ); document.write( "1 | 1 9 8 -60 \r\n" ); document.write( " | 1 10 18\r\n" ); document.write( " ------------\r\n" ); document.write( " 1 10 18 -42\r\n" ); document.write( "\r\n" ); document.write( "Nope! Remainder is -42, not 0.\r\n" ); document.write( "\r\n" ); document.write( "We try 2.\r\n" ); document.write( "\r\n" ); document.write( "2 | 1 9 8 -60 \r\n" ); document.write( " | 2 22 60\r\n" ); document.write( " ------------\r\n" ); document.write( " 1 11 30 0\r\n" ); document.write( "\r\n" ); document.write( "Aha. 2 is a rational zero.\r\n" ); document.write( "\r\n" ); document.write( "So the synthetic division tells us\r\n" ); document.write( "we have factored the polynomial as\r\n" ); document.write( "\r\n" ); document.write( "f(x)=x^3+9x^2+8x-60\r\n" ); document.write( "\r\n" ); document.write( "f(x)=(x-2)(x^2+11x+30)\r\n" ); document.write( "\r\n" ); document.write( "Now we can finish factoring that and get\r\n" ); document.write( "\r\n" ); document.write( "f(x)=(x-2)(x+6)(x+5)\r\n" ); document.write( "\r\n" ); document.write( "So the zeros are 2, -6, and -5\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |