1.

Find the LCM of x2 – 4x + 3, 2x2 – 3x + 1, and 2x2 + 7x + 3.1. (4x2 – 1)(x2 – 9)(x – 1)2. (4x2 + 1)(x2 – 9)3. (x2 – 9)(x – 1)(2x + 3)4. (4x2 + 1)(x + 1)

Answer» Correct Answer - Option 1 : (4x2 – 1)(x2 – 9)(x – 1)

Given:

x2 – 4x + 3, 2x2 – 3x + 1, and 2x2 + 7x + 3

Concept:

The LCM of two or more given polynomials is the least polynomial which is exactly divisible by each of them.

Calculation:

x2 – 4x + 3 = x2 – 3x – x + 3

⇒ x(x – 3) – 1(x – 3)

⇒ (x – 1)(x – 3)

2x2 – 3x + 1 = 2x2 – 2x – x + 1

⇒ 2x(x – 1) – 1(x – 1)

⇒ (2x – 1)(x – 1)

2x2 + 7x + 3 = 2x2 + 6x + x + 3

⇒ 2x(x + 3) + 1(x + 3)

⇒ (2x + 1)(x + 3)

LCM of x2 – 4x + 3, 2x2 – 3x + 1, and 2x2 + 7x + 3

⇒ (x – 1)(x – 3) (2x – 1)(x – 1) (2x + 1)(x + 3)

⇒ (2x – 1)(2x + 1) (x – 3)(x + 3) (x – 1)

⇒ (4x2 – 1)(x2 – 9)(x – 1)

The required LCM is (4x2 – 1)(x2 – 9)(x – 1).



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