document.write( "Question 553789: (x+11)(x-12)(x+2)>0\r
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Algebra.Com's Answer #361081 by KMST(5328) $\"\"$ $\"About$

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Each of the factors in $\"%28x%2B11%29%28x-12%29%28x%2B2%29\"$ is a linear function. Because in each factor the coefficient of x is 1, their graphs are lines of slope 1. The value of each function becomes zero for a certain value of x, is positive for greater values of x, and negative to the other side of x.
\n" ); document.write( "The zeroes of the product are the zeros for the factors, and are -11, -2, and 12.
\n" ); document.write( "Since the factors change sign (from negative to positive) at different values for x, the product function changes sign (from negative to positive, or from positive to negative) at each of the zeroes.
\n" ); document.write( "For $\"x%3C-11\"$ , all 3 factor are negative and so is their product.
\n" ); document.write( "For $\"-11%3Cx%3C-2\"$ , factor (x+11) is positive, and the other two factors are negative, making the product positive.
\n" ); document.write( "For $\"-2%3Cx%3C12\"$ , the product function is negative again, and
\n" ); document.write( "for $\"x%3E12\"$ , all 3 factors and the function are positive.
\n" ); document.write( "The solution to $\"%28x%2B11%29%28x-12%29%28x%2B2%29%3E0\"$ is the set of x values such that $\"-11%3Cx%3C-2\"$ , or $\"x%3E12\"$ .\r
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