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1)If we can factor a quadratic inequality, then the inequality can be solved with a sign graph, which shows where each factor is positive, negative, or zero.
\n" ); document.write( "for example,
\n" ); document.write( "x^2 +3x -10 > 0
\n" ); document.write( "factor polynomial
\n" ); document.write( "(x+5)*(x-2) > 0
\n" ); document.write( "This inequality says that the product of x + 5 and x - 2 is positive. If both factors are negative or both are positive, the product is positive. To analyze the signs of each factor, we make a sign graph. First consider the possible values of the factor x + 5
\n" ); document.write( "x+5=0 if x=-5 put 0 above -5 on number line
\n" ); document.write( "x+5>0 if x>-5 put + to the right of -5
\n" ); document.write( "x+5<0 if x<-5 put - to the left of -5
\n" ); document.write( "now do the same analysis for x-2=0, x-2>0, x-2<0
\n" ); document.write( "2) First determine zeros for the polynomial in 1
\n" ); document.write( "(x+5)*(x-2) = 0 and
\n" ); document.write( "zeros are -5 and 2
\n" ); document.write( "To solve by the Test-Point Method, pick a sample point in each interval, the intervals being (negative infinity, –5), (-5, 2), (2, positive infinity)
\n" ); document.write( "remember that our inequality from 1 is
\n" ); document.write( "x^2 +3x -10 > 0
\n" ); document.write( "evaluate the inequality for each test point and
\n" ); document.write( "(note that we are interested in the interval/s that give us a positive value)
\n" ); document.write( "If the rational expression is greater than 0, then we are interested in values that cause our rational expression to be positive.
\n" ); document.write( "3) both methods use the sign of evaluated expressions to find the solution set. \n" ); document.write( "