# SOLUTION: If f(x) = x(x + 1)(x – 4), use interval notation to give all values of x where f(x) > 0. a. (–1, 4) b. (–1, 0) &#8746; (4, &#8734;) c. (–1, 4) d. (0, 1) &#8746; (4, &#8734;)

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: If f(x) = x(x + 1)(x – 4), use interval notation to give all values of x where f(x) > 0. a. (–1, 4) b. (–1, 0) &#8746; (4, &#8734;) c. (–1, 4) d. (0, 1) &#8746; (4, &#8734;)      Log On

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 Question 107005: If f(x) = x(x + 1)(x – 4), use interval notation to give all values of x where f(x) > 0. a. (–1, 4) b. (–1, 0) ∪ (4, ∞) c. (–1, 4) d. (0, 1) ∪ (4, ∞)Answer by Fombitz(13828)   (Show Source): You can put this solution on YOUR website! Let's look at the key x values and determine the sign of f(x). At x=0, f(x)=0 That knocks out a and c because they include x=0 (they're the same answer?). Since both b and d include x>4, we won't look at that. Anyways when x>4, f(x)>0 because x>0, x+1>0, and x-4>0. The two other regions to choose are (-1,0) and (0,1). b.)If you choose a point between (-1,0), say x=-1/2, then x<0, because -1/2<0. x+1>0, because -1/2+1=1/2>0 x-4<0. The product would then be negative times positive times negative. The product (f(x)) would be positive. d.)If you choose a point between (0,1), say x=1/2, then x>0, because 1/2>0. x+1>0, because 1/2+1=1/2>0 x-4<0. The product would then be positive times positive times negative. The product (f(x)) would be negative. The answer is b. b. (–1, 0) ∪ (4, ∞)