Advanced Math practice question

Answer: A. x < 1 or 3 < x < 5

The sign changes at each zero. For x > 5 all three factors are positive; between 3 and 5 one is negative; between 1 and 3 two are negative (positive product); below 1 all three are negative. So h < 0 for x < 1 and for 3 < x < 5.

Why the other answers are wrong

B. 1 < x < 3 or x > 5

Those are the intervals where h(x) > 0.

C. x < 1 only

Misses the interval 3 < x < 5.

D. 1 < x < 5

h(2) = (1)(−1)(−3) = 3 > 0, so not all of 1 < x < 5.

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