- 2x - 3y - 4
- 2x + 3y - 4
- 2x + 3y - 5
- 2x - 3y + 5

Option 2 : 2x + 3y - 4

**Given:**

4x2 + 9y2 + 12xy + 2x + 3y - 20

**Formula used:**

(a + b)^{2} = a^{2} + b^{2} + 2ab

**Calculations:**

Simplifying the given polynomial,

⇒ 4x2 + 9y2 + 12xy + 2x + 3y - 20

⇒ (2x + 3y)^{2} + 2x + 3y - 20

Let (2x + 3y) = a

⇒ a^{2} + a - 20 = 0

Solving by splitting the middle term,

⇒ a2 + 5a - 4a - 20 = 0

⇒ a(a + 5) - 4(a + 5) = 0

⇒ (a - 4)(a + 5) = 0

Substituting the value of a,

(2x + 3y - 4)(2x + 3y + 5) are the two factors of the given polynomial

**∴ Amongst the given options, 2x + 3y - 4 is one factor of the given polynomial**

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