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Question

If x4 is a factor of p(x)=3x3+4x+k, which of the following statements is true ?

A
k = 208
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B
k = -208
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C
k is a positive integer
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D
2k - 2 = -418
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Solution

The correct options are
B k = -208
D 2k - 2 = -418
Given, x4 is a factor of p(x).
By factor theorem, we have p(4)=0.
3(43)+4(4)+k=0
208+k=0
k=208
k is not a positive integer.
And, 2k2=2(208)2=418

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