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The H.C.F. of the polynomials 20x2 – 9x + 1 and 5x2 – 6x + 1, is:
1. x – 1
2. 5x – 1
3. 4x – 1
4. 5x + 1

1 Answer

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Best answer
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) 

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