# SOLUTION: i dont understand how to put this in interval notation. (x^2+2x-8/x+1) less than or equal to 0. i get to x=-4 x=2 x=-1 just need help putting it in interval notation. thanks!

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: i dont understand how to put this in interval notation. (x^2+2x-8/x+1) less than or equal to 0. i get to x=-4 x=2 x=-1 just need help putting it in interval notation. thanks!      Log On

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 469720: i dont understand how to put this in interval notation. (x^2+2x-8/x+1) less than or equal to 0. i get to x=-4 x=2 x=-1 just need help putting it in interval notation. thanks!Answer by ccs2011(207)   (Show Source): You can put this solution on YOUR website!Ok first off notice when x = -1, the function becomes undefined So when stating the domain, do not include x = -1. Yes you have correctly identified the zeroes, x=-4 and x = 2. But when is the function less than zero. There are 3 factors to consider: x+4 < 0 --> x < -4 x-2 < 0 --> x < 2 x+1 < 0 --> x < -1 **Note: Multiplying/Dividing 2 negative numbers equal a positive number** When x < -4, it satisfies all 3 conditions making each factor negative thus making the entire expression negative When -4 < x < -1, it satisfies 2 conditions making 2 factors negative thus making entire expression positive When -1 < x < 2, it satisfies 1 condition making 1 factor negative thus making entire expression negative When x > 2, all factors are positive thus expression is positive Therefore, expression is less than or equal to zero when x <= -4 and -1 < x <= 2 In interval notation, use brackets and parenthesis instead of "<" symbols Domain: (,-4]U(-1,2]