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Question

Check whether p(x) = x3​ + 5x2 + 2x - 5 is a multiple of g(x) = x + 2.


A

p(x) is a multiple of g(x)

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B

p(x) is not a multiple of g(x)

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C

g(x) is a multiple of p(x)

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D

g(x) is not a multiple of p(x)

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Solution

The correct option is B

p(x) is not a multiple of g(x)


Consider p(x) = x3​ + 5x2 + 2x5

If p(-2) = 0, then g(x) is a factor of p(x) which implies p(x) is a multiple of g(x)

p(-2) = 23​ + 5(2)2​ + 2(-2) - 5 = - 8 + 20 - 4 - 5 = 3 ≠ 0

Therefore, p(x) is not a multiple of g(x).


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