Question

The degree of the polynomial (x + 1)(x² − x + x ⁴− 1) is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The Correct Option is D

We are given the polynomial: \[ (x + 1) \cdot (x^2 - x + x^4 - 1) \] To find the degree of the polynomial, we will first expand it. The degree of the polynomial is determined by the highest power of \( x \) after expansion. Let’s expand the expression: \[ (x + 1)(x^2 - x + x^4 - 1) \] When we multiply the terms, we get: \[ = x(x^2 - x + x^4 - 1) + 1(x^2 - x + x^4 - 1) \] \[ = x^3 - x^2 + x^5 - x + x^2 - x + x^4 - 1 \] Now, combine like terms: \[ = x^5 + x^4 + x^3 - 2x - 1 \] The highest power of \( x \) is \( x^5 \), so the degree of the polynomial is 5.

The correct option is (D): \(5\)