1.

The factors of 3(x + 2)2 + 5(x + 2) + 2 are:1. (3x + 5)(x + 2)2. (3x + 8)(x + 3)3. (3x + 8)(x + 5)4. (3x + 1)(x + 2)

Answer» Correct Answer - Option 2 : (3x + 8)(x + 3)

Given:

Our given expression is 3(x + 2)2 + 5(x + 2) + 2

Calculation:

Our given expression is 3(x + 2)2 + 5(x + 2) + 2

Let (x + 2) be t, then our given equation becomes,

3t2 + 5t + 2

⇒ 3t2 + 3t + 2t + 2

⇒ 3t(t + 1) + 2(t + 1)

⇒ (3t + 2)(t + 1)

Putting the value of t,

{3(x + 2) + 2}{(x + 2) + 1}

⇒ (3x + 6 + 2)(x + 3)

⇒ (3x + 8)(x + 3)

∴ The factor of the given expression is (3x + 8)(x + 3)


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