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Question

Statement 1: The polynomial P(x)=4x3–3x2+5x–6 when divided by x–1 gives zero as the remainder.

Statement 2: (x–1) is a factor of the polynomial P(x)=4x3–3x2+5x–6.


A

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

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B

Both the statements are true and 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 A

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


According to factor theorem when a polynomial P(x) gives zero as the remainder when divided by (x – a), where ‘a’ is any real number, then (x – a) is the factor of the polynomial P(x).

For the given polynomial P(x)=4x33x2+5x6
P(1)=4(1)33(1)2+5(1)6=0

Since P(1)=0, (x-1) is a factor of P(x).
When P(x) is divided by (x-1), the remainder will be zero.
Thus, statement 2 is the correct explanation to statement 1.


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