Statement 1: A polynomial P(x) of degree greater than or equal to one, when divided by x – a, leaves a remainder zero.

Statement 2: x – a is a factor of the polynomial P(x).

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

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

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Statement 1 is true and statement 2 is false

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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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Similar questions

Statement 1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement 2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

The polynomial x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8 when divided by (x + 1) leaves a remainder of 14 .

The value of the polynomial x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8 at x = - 1 is 14.

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

Choose the correct option.

Statement $1 : (p \land \sim q) \land (\sim p \land q)$ is a fallacy.

Statement $2 : (p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow\sim p)$ is a tautology.

C - O

C - O