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Positive values of (1-|x|)(1+x)

Source: 1976 AHSME Problem 7

May 15, 2014
functionalgebrapolynomialAMC

Problem Statement

If xx is a real number, then the quantity (1−∣x∣)(1+x)(1-|x|)(1+x) is positive if and only if
<spanclass=′latex−bold′>(A)</span>∣x∣<1<spanclass=′latex−bold′>(B)</span>∣x∣>1<spanclass=′latex−bold′>(C)</span>x<−1 or −1<x<1<span class='latex-bold'>(A) </span>|x|<1\qquad<span class='latex-bold'>(B) </span>|x|>1\qquad<span class='latex-bold'>(C) </span>x<-1\text{ or }-1<x<1\qquad
<spanclass=′latex−bold′>(D)</span>x<1<spanclass=′latex−bold′>(E)</span>x<−1<span class='latex-bold'>(D) </span>x<1\qquad <span class='latex-bold'>(E) </span>x<-1
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