Question

# Statement 1: The polynomial P(x)=4x3â€“3x2+5xâ€“6 when divided by xâ€“1 gives zero as the remainder. Statement 2: (xâ€“1) is a factor of the polynomial P(x)=4x3â€“3x2+5xâ€“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)=4x3–3x2+5x–6 P(1)=4(1)3–3(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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