document.write( "Question 932817: The equation is f(x)=2x^3-2x^2-40x. I understand that you make this equal to 0. Then you would get X=0, x=-4, x=5. But I don't understand how you get the table to graph the rest. And how would you write the result? \n" ); document.write( "

Algebra.Com's Answer #566395 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=2x%28x%5E2-x-20%29\"$ and the roots are 0, -4, 5. The roots are the x values where the function f either touches or crosses the x-axis. The roots cut the x-axis into four intervals on which you can test the sign of f in each interval. You can simply pick an x value in each interval, and check the resulting sign for f.\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=2x%28x%2B4%29%28x-5%29\"$ , the function in completely factored form.\r
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\n" ); document.write( "\n" ); document.write( "INTERVAL_________________________SIGN of f
\n" ); document.write( " $\"x%3C-4\"$ _________________(-)(-)(-), NEGATIVE
\n" ); document.write( " $\"-4%3Cx%3C0\"$ _______________(-)(+)(-), POSITIVE
\n" ); document.write( " $\"0%3Cx%3C5\"$ ________________(+)(+)(-), NEGATIVE
\n" ); document.write( " $\"x%3E5\"$ __________________(+)(+)(+), POSITIVE\r
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\n" ); document.write( "\n" ); document.write( "This table indicates the graph of f(x) CROSSING the x-axis at every root. This helps in forming the graph. \n" ); document.write( "

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