document.write( "Question 393464: what is the step by step process of solving this polynomial by factoring?
\n" ); document.write( "27x^3+125=0 \n" ); document.write( "

Algebra.Com's Answer #279256 by Earlsdon(6294) $\"\"$ $\"About$

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Facor:
\n" ); document.write( " $\"27x%5E3%2B125+=+0\"$ Did you notice that you have the sum of two cubes?
\n" ); document.write( " $\"%283x%29%5E3%2B%285%29%5E3+=+0\"$
\n" ); document.write( "The sum of two cubes can be factored thus:
\n" ); document.write( " $\"A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\"$
\n" ); document.write( "In your problem, A = 3x and B = 5, so...
\n" ); document.write( " $\"27x%5E3%2B125+=+0\"$ becomes:
\n" ); document.write( " $\"%283x%2B5%29%289x%5E2-15x%2B25%29+=+0\"$ Apply the zero product rule:
\n" ); document.write( " $\"3x%2B5+=+0\"$ or $\"9x%5E2-15x%2B25+=+0\"$
\n" ); document.write( "Do the first factor:
\n" ); document.write( " $\"3x%2B5+=+0\"$ Subtract 5.
\n" ); document.write( " $\"3x+=+-5\"$ Divide by 3.
\n" ); document.write( " $\"x%5B1%5D+=+-5%2F3\"$
\n" ); document.write( "Do the second factor:
\n" ); document.write( " $\"9x%5E2-15x%2B25+=+0\"$ Use the quadratic formula to solve: $\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ and a = 9, b = -15, and c = 25.
\n" ); document.write( " $\"x+=+%28-%28-15%29%2B-sqrt%28%28-15%29%5E2-4%289%29%2825%29%29%29%2F2%289%29\"$
\n" ); document.write( " $\"x+=+%2815%2B-sqrt%28225-900%29%29%2F18\"$
\n" ); document.write( " $\"x+=+%2815%2B-sqrt%28-675%29%29%2F18\"$ and when you work this out, you should get:
\n" ); document.write( " $\"x%5B2%5D+=+0.833%2B1.44i\"$ and $\"x%5B3%5D+=+0.833-1.44i\"$ \n" ); document.write( "

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