document.write( "Question 1061025: Solve the inequality.\r
\n" ); document.write( "\n" ); document.write( "(x - 5)(x^2 + x + 1) > 0
\n" ); document.write( " a. (-∞, -1) or (1, ∞)
\n" ); document.write( " b. (-1, 1)
\n" ); document.write( " c. (-∞, 5)
\n" ); document.write( " d. (5, ∞)
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Algebra.Com's Answer #675869 by josgarithmetic(39617) $\"\"$ $\"About$

You can put this solution on YOUR website!
The quadratic factor is positive everywhere.
\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "You could try putting it into standard form, or you can just check its discriminant to see if this is negative or not. You should find that the discriminant,,...... $\"1%5E2-4%2A1%2A1=1-4=-3%3C0\"$ , so this means the quadratic factor as a function will not have points on the x-axis....\r
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\n" ); document.write( "\n" ); document.write( "That then leaves you with the critical x value for the linear factor, and that is at x=5.\r
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\n" ); document.write( "\n" ); document.write( " $\"linearFactor%2AquadraticFactor%3E0\"$ ;
\n" ); document.write( "Check the signs in the indicated intervals to see which interval makes the inequality true and which make it false.\r
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document.write( "INTERVAL          ANALYZE INEQUALITY     RESULT\r\n" );
document.write( "(-infin,5)        (-)(+)>0,  FALSE       FALSE\r\n" );
document.write( "(5,infinity)      (+)(+)>0,  TRUE        TRUE\r\n" );
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