Question

Assertion (A): x³ + 2x² – x – 2 is a polynomial of degree 3.

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

Options

• Both A and R are correct and R is the correct explanation for A.

• Both A and R are correct and R is not the correct explanation for A.

• A is true, but R is false.

• Both A and R are true.

Answer 1

Both A and R are correct and R is not the correct explanation for A.

Explanation:

A is true because the highest power of x is 3 (degree = 3).

R is true because f(–2) = (–2)³ + 2(–2)² – (–2) – 2 

= –8 + 8 + 2 – 2 

= 0

So, x + 2 is a factor. 

However, R is not the reason for A having x + 2 as a factor doesn’t explain why the polynomial’s degree is 3.