document.write( "Question 43596This question is from textbook Algebra and trigonometry with analytic geometry
\n" ); document.write( ": If f(x)=x(x-1)(x-4)^2, use interval notation to give all values of x where f(x)>0. My answer is (-infty,0) u (1,4) u (4,infty) is this right. thanks again. \n" ); document.write( "

Algebra.Com's Answer #28666 by psbhowmick(878) $\"\"$ $\"About$

You can put this solution on YOUR website!
So you are right!\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%28x-1%29%28x-4%29%5E2\"$
\n" ); document.write( "For all real values of 'x', $\"%28x-4%29%5E2+%3E+0\"$ except when x = 4.
\n" ); document.write( "So, for f(x) to be greater than 0, $\"x%28x-1%29%3E0\"$ .
\n" ); document.write( "This is possible if\r
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\n" ); document.write( "\n" ); document.write( "1) Case I
\n" ); document.write( "both x > 0 and (x - 1) > 0 which implies x > 1 [as x > 1 automatically satisfy both the conditions]\r
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\n" ); document.write( "\n" ); document.write( "2) Case II
\n" ); document.write( "both x < 0 and (x - 1) < 0 which implies x < 0 [as x < 0 automatically satisfy both the conditions]\r
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\n" ); document.write( "\n" ); document.write( "So for f(x) > 0, either x > 1 [from Case I] or x < 0 [from Case II]; also x not equal to 4.
\n" ); document.write( "Hence, the answer is (- $\"infinity\"$ ,0)U(1,4)U(4, $\"infinity\"$ ). \n" ); document.write( "

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