document.write( "Question 718531: For the polynomial below,3 is a zero
\n" ); document.write( "G(X)=x^3-5x^2+2x+12
\n" ); document.write( "Express as a product of linear factors. \n" ); document.write( "

Algebra.Com's Answer #440957 by KMST(5328) $\"\"$ $\"About$

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If $\"3\"$ is a zero of $\"G%28x%29=x%5E3-5x%5E2%2B2x%2B12\"$
\n" ); document.write( " $\"%28x-3%29\"$ is one of the linear factors we are searching for.
\n" ); document.write( "Dividing $\"G%28x%29\"$ by $\"%28x-3%29\"$ we find
\n" ); document.write( " $\"G%28x%29=%28x-3%29%28x%5E2-2x-4%29\"$
\n" ); document.write( "Now we just have to factor $\"%28x%5E2-2x-4%29\"$
\n" ); document.write( "Unfortunately, the factors are not pretty.
\n" ); document.write( "Using the quadratic formula, or by \"completing the square\"
\n" ); document.write( "we find that the solutions to $\"x%5E2-2x-4=0\"$ are
\n" ); document.write( " $\"x=1+%2B-+sqrt%285%29\"$
\n" ); document.write( "That means that we can factor $\"x%5E2-2x-4\"$ as
\n" ); document.write( " $\"x%5E2-2x-4=%28x-1-sqrt%285%29%29%28x-1%2Bsqrt%285%29%29\"$ and
\n" ); document.write( " $\"highlight%28G%28x%29=%28x-3%29%28x-1-sqrt%285%29%29%28x-1%2Bsqrt%285%29%29%29\"$ \n" ); document.write( "

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