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{:(x,-5,-3,-1,1),(y,0,4,-3,0):} Four p...

`{:(x,-5,-3,-1,1),(y,0,4,-3,0):}`
Four points on the graph of a polynomial P are shown in the table above. If P is a polynomial of degree 3, then P(x) could equal

A

a(x-5)(x-2)(x+1)

B

a(x-5)(x+2)(x+1)

C

a(x+5)(x-2)(x-1)

D

a(x+5)(x+2)(x-1)

Text Solution

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The correct Answer is:
D
Since -5 and 1 are both zeros, (x+5) and (x-1) are factors of P(x). Since P(x) changes sign between x=-3 and x=-1, there is a zero between these two values. Choice D is the only one that meets all three criteria.
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