document.write( "Question 112057: I have to solve the equation by factoring first and then applying the zero product principle. so, can someone help me solve x^3 +x^2-7x=7. any help would be appreciated. \n" ); document.write( "

Algebra.Com's Answer #81781 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Factor:
\n" ); document.write( " $\"x%5E3%2Bx%5E2-7x+=+7\"$ Subtract 7 from both sides.
\n" ); document.write( " $\"x%5E3%2Bx%5E2-7x-7=+0\"$ Factor by grouping.
\n" ); document.write( " $\"%28x%5E3%2Bx%5E2%29+-+%287x%2B7%29+=+0\"$ Factor $\"x%5E2\"$ from the first group and 7 from the second group.
\n" ); document.write( " $\"x%5E2%28x%2B1%29+-+7%28x%2B1%29=+0\"$ Now factor the common factor of $\"%28x%2B1%29\"$
\n" ); document.write( " $\"%28x%2B1%29%28x%5E2-7%29+=+0\"$ Now apply the zero products principle.
\n" ); document.write( " $\"x%2B1+=+0\"$ or $\"x%5E2-7+=+0\"$
\n" ); document.write( "If $\"x%2B1+=+0\"$ then $\"x+=+-1\"$
\n" ); document.write( "if $\"x%5E2-7+=+0\"$ then $\"x%5E2+=+7\"$ so $\"x+=+sqrt%287%29\"$ or $\"x+=+-sqrt%287%29\"$
\n" ); document.write( "The three roots are:
\n" ); document.write( " $\"x+=+-1\"$
\n" ); document.write( " $\"x+=+sqrt%287%29\"$
\n" ); document.write( " $\"x+=+-sqrt%287%29\"$ \n" ); document.write( "

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