Correct Answer - Option 2 : 5x – 1
Calculation:
Our given expression is 20x2 – 9x + 1 and 5x2 – 6x + 1
Factors of 20x2 – 9x + 1
⇒ 20x2 – 9x + 1
⇒ 20x2 – 5x – 4x + 1
⇒ 5x(4x – 1) – 1(4x – 1)
⇒ (5x – 1)(4x – 1)
And, Factor of 5x2 - 6x + 1
⇒ 5x2 – 6x + 1
⇒ 5x2 – 5x - x + 1
⇒ 5x(x – 1) –1(x – 1)
⇒ (5x –1)(x – 1)
The HCF of 20x2 – 9x + 1 and 5x2 – 6x + 1 = (5x – 1)
∴ The HCF of 20x2 – 9x + 1 and 5x2 – 6x + 1 is (5x – 1)