document.write( "Question 107005: If f(x) = x(x + 1)(x – 4), use interval notation to give all
\n" ); document.write( "values of x where f(x) > 0.\r
\n" ); document.write( "\n" ); document.write( "a. (–1, 4)
\n" ); document.write( "b. (–1, 0) ∪ (4, ∞)
\n" ); document.write( "c. (–1, 4)
\n" ); document.write( "d. (0, 1) ∪ (4, ∞) \n" ); document.write( "

Algebra.Com's Answer #77961 by Fombitz(32388) $\"\"$ $\"About$

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\n" ); document.write( "Let's look at the key x values and determine the sign of f(x).
\n" ); document.write( "At x=0, f(x)=0
\n" ); document.write( "That knocks out a and c because they include x=0 (they're the same answer?).
\n" ); document.write( "Since both b and d include x>4, we won't look at that.
\n" ); document.write( "Anyways when x>4, f(x)>0 because x>0, x+1>0, and x-4>0.
\n" ); document.write( "The two other regions to choose are (-1,0) and (0,1).
\n" ); document.write( "b.)If you choose a point between (-1,0), say x=-1/2, then
\n" ); document.write( "x<0, because -1/2<0.
\n" ); document.write( "x+1>0, because -1/2+1=1/2>0
\n" ); document.write( "x-4<0.
\n" ); document.write( "The product would then be negative times positive times negative.
\n" ); document.write( "The product (f(x)) would be positive.
\n" ); document.write( "d.)If you choose a point between (0,1), say x=1/2, then
\n" ); document.write( "x>0, because 1/2>0.
\n" ); document.write( "x+1>0, because 1/2+1=1/2>0
\n" ); document.write( "x-4<0.
\n" ); document.write( "The product would then be positive times positive times negative.
\n" ); document.write( "The product (f(x)) would be negative.
\n" ); document.write( "The answer is b.
\n" ); document.write( "b. (–1, 0) ∪ (4, ∞)
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-2%2C+5%2C+-20%2C+20%2C+x%2A%28x%2B1%29%2A%28x-4%29%29\"$ \n" ); document.write( "

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