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If we define the expression $P(x)=x^2$ and an expression $Q(x) = |4x|$, then for how many integer values is $P(x) -Q(x)$ a positive quantity?

$ a)2 \quad\quad\quad b) 4 \quad\quad c) 6 \quad\quad\quad d)8$

We have to find $P(x)-Q(x) \gt 0 \Rightarrow x^2 -|4x| \gt 0 \Rightarrow x>4 \; or \; x < -4 \; $ but this means there are infinitely many possible values, what exactly am I missing here?

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As you say $x^2 -|4x| \gt 0$ when $x \gt 4$ or $x \lt -4$ , so except for the nine integers $-4,-3,-2,-1,0,1,2,3,4$.

So my guess is that there is some error in the question either as written or as you have copied it

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Wolfram agrees on $x<-4$. –  Quixotic Mar 3 '12 at 14:18
    
@Foool: my mistake - I have corrected it –  Henry Mar 3 '12 at 14:20
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