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Question

# Statement 1: A polynomial P(x) of degree greater than or equal to one, when divided by x â€“ a, leaves a remainder zero. Statement 2: x â€“ a is a factor of the polynomial P(x).

A

Both the statements are true and statement 1 is the correct explanation of statement 2.

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B

Both the statements are true but statement 2 is not the correct explanation of statement 1.

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C

Statement 1 is true and statement 2 is false

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D

Statement 1 is false and statement 2 is true

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Solution

## The correct option is C Statement 1 is true and statement 2 is false As per factor theorem, when a polynomial P(x) of degree greater than or equal to one exists such that P(a) = 0, x – a is the factor of the polynomial P(x). Conversley, if x – a is a factor of the polynomial P(x) then P(a) = 0.

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