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You can put this solution on YOUR website!
\n" ); document.write( "In the solution by tutor @mathlover1, she identified the values of x that make each of the individual factors negative or zero; but it is unclear how she used that information to identify the intervals on which the complete expression is negative or zero.
\n" ); document.write( "Consider the polynomial function
\n" ); document.write( "
\n" ); document.write( "We want to identify when the function value is zero or negative.
\n" ); document.write( "Clearly the function value is zero at x=-5, x=2, and x=7.
\n" ); document.write( "To identify the intervals on which the function value is negative, there are several options. Among those options are
\n" ); document.write( "(1) The function is a cubic with positive leading coefficient. Think of what the graph of that kind of function looks like. The function value is negative for \"large negative\" value of x and positive for large positive values of x. That, along with the known zeros of the function, will determine the intervals on which the function value is negative.
\n" ); document.write( "(2) Choose a test point in each of the intervals determined by the zeros of the function to see whether the function value is positive or negative in each interval.
\n" ); document.write( "(3) (My personal choice....) You know that for large negative values of x all three factors are negative, so the function value is negative to the left of x=-5. Then, as you \"walk\" along the number line to the right, the function value changes sign each time you pass one of the zeros. So the function value is (a) negative for x less than -5; (b) positive for x between -5 and 2; (c) negative for x between 2 and 7; and (d) positive for x greater than 7. \n" ); document.write( "