document.write( "Question 1112466: Hi,
\n" ); document.write( "Please help me to solve step-by-step on these questions.
\n" ); document.write( "Thank you very much.
\n" ); document.write( "3. Factor the following polynomial by Grouping : (Show all work) Explain how to know when to factor out a negative sign from the last two terms.
\n" ); document.write( " 12x^3 + 15x^2 – 8x – 10\r
\n" ); document.write( "\n" ); document.write( "4. What are the steps to find the domain of a rational function ? Apply the process to the following rational function and state the domain using set notation :
\n" ); document.write( " f(x) =(3x^2+2x-7)/(2x^3-x^2-x)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #727495 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "3)   = group the terms =  -  =  -  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Done.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "4)  What are the steps to find the domain of a rational function ?\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Answer.  \r\n" );
document.write( "\r\n" );
document.write( "    A rational function is the ratio of two polynomials.\r\n" );
document.write( "\r\n" );
document.write( "    To find the domain of the rational function, you need\r\n" );
document.write( "\r\n" );
document.write( "        a) to consider its DENOMINATOR.\r\n" );
document.write( "\r\n" );
document.write( "        b) to find the roots of the polynomial in the denominator\r\n" );
document.write( "\r\n" );
document.write( "              (that make the denominator equal to zero !)\r\n" );
document.write( "\r\n" );
document.write( "        c) then exclude these roots from the set of all real numbers (from the number line).\r\n" );
document.write( "\r\n" );
document.write( "           The remained set of real numbers is the domain of the given rational function.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    In your case, you need to consider the denominator 2x^3-x^2-x.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It is the polynomial of the third degree.\r\n" );
document.write( "\r\n" );
document.write( "    You can factor it in this way  2x^3-x^2-x = x*(2x^2 - x -1) = x*(2x+1)*(x-1).\r\n" );
document.write( "\r\n" );
document.write( "    The roots are  x= 0,  x= -1/2  and  x= 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     So, the domain of the given rational function is the set of all real numbers except -1/2, 0 and 1  (listed in ascending order).\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "I answered all your questions.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );