document.write( "Question 324761: Find all the rational zeros of f(x) = 6x^3–3x+11x^2–2. \n" ); document.write( "

Algebra.Com's Answer #232656 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+graph%28+300%2C+300%2C+-3%2C+3%2C+-10%2C+10%2C++6x%5E3-3x%2B11x%5E2-2%29\"$
\n" ); document.write( "Looks like $\"highlight%28x=-2%29\"$ is a zero, verify using the equation.
\n" ); document.write( " $\"6%28-8%29-3%28-2%29%2B11%284%29-2=-48%2B6%2B44-2=0\"$
\n" ); document.write( "You can guess the other two or you can use polynomial long division to get the remaining quadratic equation.
\n" ); document.write( " $\"%286x%5E3-3x%2B11x%5E2-2%29%2F%28x%2B2%29=6x%5E2-x-1\"$
\n" ); document.write( "You can then factor this quadratic,
\n" ); document.write( " $\"6x%5E2-x-1=%283x%2B1%29%282x-1%29\"$
\n" ); document.write( "Which yields,
\n" ); document.write( " $\"3x%2B1=0\"$
\n" ); document.write( " $\"3x=-1\"$
\n" ); document.write( " $\"highlight%28x=-1%2F3%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"2x-1=0\"$
\n" ); document.write( " $\"2x=1\"$
\n" ); document.write( " $\"highlight%28x=1%2F2%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );