Question

Assertion (A): $$x^3 + 2x^2 - x - 2$$ is a polynomial of degree 3.

Reason (R): $$x + 2$$ is a factor of the polynomial.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, but R is not the correct explanation of A.

Explanation:

The polynomial has highest power 3, so its degree is 3; A is true. Also $$f(-2) = (-2)^3 + 2(-2)^2 - (-2) - 2 = 0$$, so $$x + 2$$ is a factor, making R true. But R does not explain the degree of the polynomial.