document.write( "Question 94403: Factor completely 125x^6+x^3 \n" ); document.write( "

Algebra.Com's Answer #68760 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Factor completely 125x^6+x^3
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\n" ); document.write( "Factor out x^3 and you have:
\n" ); document.write( "x^3(125x^3 + 1)
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\n" ); document.write( "You should recognize (125x^3 + 1) as the sum of cubes. (125 = 5^3 and 1^3 is 1)
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\n" ); document.write( "In your algebra book somewhere they should have, check the index for:
\n" ); document.write( "\"Sum of cubes\": a^3 + b^3 = (a + b)(a^2 - ab + b^2)
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\n" ); document.write( "Applying this to 125x^3 + 1, we have:
\n" ); document.write( " (5x + 1) (25x^2 - 5x + 1)
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\n" ); document.write( "Include the x^3, that we factored out earlier and we have:
\n" ); document.write( "x^3 (5x + 1) (25x^2 + 5x + 1)
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\n" ); document.write( "Did this make sense to you? \n" ); document.write( "

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