Question

The HCF of the polynomials \( 2x^3 + 5x^2 - 2x - 5 \) and \( 3x^3 - x^2 - 3x + 1 \) is:

• A. \( x^2 - 1 \)
• B. \( x + 1 \)
• C. \( x - 1 \)
• D. \( (x + 3)(2x + 5) \)

Hint:

To find the HCF of polynomials, use polynomial division and find the common factor in both expressions.

Answer 1

The Correct Option is A

Given polynomials: \[ P_1(x) = 2x^3 + 5x^2 - 2x - 5 \] \[ P_2(x) = 3x^3 - x^2 - 3x + 1 \] Using the polynomial division method, we find that the remainder is: \[ x^2 - 1 \]
Thus, the HCF of both polynomials is: \[ x^2 - 1 = (x - 1)(x + 1) \]
Thus, the correct answer is \( x^2 - 1 \).