Question

What is the H.C.F of (2x³ + x² – 5x + 2) and (x² + 2x – 3)?
1. (x – 1)
2. (x – 2)
3. (x + 1)
4. (x + 2)

Answer 1

Correct Answer - Option 1 : (x – 1)

Factors of (2x³ + x² – 5x + 2)

⇒ (x - 1) (2x² + 3x – 2)

⇒ (x – 1) (2x² + 4x – x – 2)

⇒ (x - 1) [2x(x + 2) - 1(x + 2)]

⇒ (x -1) (2x -1) (x + 2)

Factors of (x ² + 2x - 3)

⇒ x² + 3x – x – 3

⇒ x(x + 3) -1(x + 3)

⇒ (x – 1) (x + 3)

(x - 1) is common in both the factors.

So, H.C.F is (x -1)