document.write( "Question 121010: How do I simplify this fraction? How do I factor a four-term polynomial?\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E3%2B2x%5E2%2B3x-6%29%2F%28x-1%29\"$ \n" ); document.write( "

Algebra.Com's Answer #88766 by nabla(475) $\"\"$ $\"About$

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The most straightforward way to simplify such a fraction is to perform long division. Normally, we would factor a 4-term polynomial by grouping, but sometimes it can be more cumbersome in comparison to long division (if that's possible!)\r
\n" ); document.write( "\n" ); document.write( "In any case, I will offer you another method that may be new to you. However, it is very powerful, and leads to the correct answer.\r
\n" ); document.write( "\n" ); document.write( "Notice that the simplification that we seek is of the form $\"ax%5E2%2Bbx%2Bc\"$ (We know there will be no remainder as it is implied by the problem that it is able to be simplified). But, we are given the factor of $\"x-1\"$ . So, let's multiply this by our general form:\r
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\n" ); document.write( "\n" ); document.write( "Now, polynomials are equivalent when their coefficients are equivalent, so we equate the coefficients we just found to the coefficients of the numerator of the problem:
\n" ); document.write( "1) $\"a=1\"$
\n" ); document.write( "2) $\"b-a=2\"$ implies $\"b=3\"$
\n" ); document.write( "3) $\"c-b=3\"$ implies $\"c=6\"$
\n" ); document.write( "4) $\"-c=-6\"$ follows $\"c=6\"$ \r
\n" ); document.write( "\n" ); document.write( "Thus, we can use these coefficients in our \"general form\" above to see that the simplification of the problem is:
\n" ); document.write( " $\"%28x%5E2%2B3x%2B6%29\"$ . \r
\n" ); document.write( "\n" ); document.write( "In any case, using long division is the preference when the specific grouping isn't obvious. \n" ); document.write( "

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