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if f(x) = x(x+3)(x-1), use interval notation to give all values of x where
\n" ); document.write( "f(x)>0.
\n" ); document.write( "To find the possible intervals, set each term equal to 0 and solve for x:
\n" ); document.write( "x=0 or x+3=0 or x-1=0
\n" ); document.write( "x=0 or x+3-3=0-3 or x-1+1=0+1
\n" ); document.write( "x=0 or x=-3 or x=1
\n" ); document.write( "The possible intervals are (-infinity,-3) or (-3,0) or (0,1) or (1,infinity).
\n" ); document.write( ":
\n" ); document.write( "For (-infinity,-3), let x=-4 and see if the outcome is positive (>0).
\n" ); document.write( "f(-4)=-4(-4+3)(-4-1)=-4(-1)(-5)=-20 This interval is NOT >0.
\n" ); document.write( ":
\n" ); document.write( "For (-3,0), let x=-1
\n" ); document.write( "f(-1)=-1(-1+3)(-1-1)=-1(2)(-2)=4 This interval IS >0.
\n" ); document.write( ":
\n" ); document.write( "For (0,1), let x=.5
\n" ); document.write( "f(.5)=.5(.5+3)(.5-1)=.5(3.5)(-5.)=-.875 This interval is NOT >0.
\n" ); document.write( ":
\n" ); document.write( "For (1,infinity) let x=2
\n" ); document.write( "f(2)=2(2+3)(2-1)=2(5)(1)=10 This interval IS >0.
\n" ); document.write( ":
\n" ); document.write( "Therefore the solution is: (-3,0)U(1,infinity)
\n" ); document.write( "Happy Calculating!!!!! \n" ); document.write( "