Questions: Algebra 2 Sem1 Quiz 2.2.1 - Factoring Factor completely: 9 x^2 + 12 x + 4 a. (2 x + 3)^2 b. (3 x + 2)^2 c. (3 x + 2)(3 x - 2) d. (2 x + 3)(3 x + 2)

Factor the quadratic expression \(9x^{2} + 12x + 4\) completely.

Identify the quadratic form

The given expression is a quadratic trinomial of the form \(ax^{2} + bx + c\), where \(a = 9\), \(b = 12\), and \(c = 4\).

Check if it is a perfect square trinomial

A perfect square trinomial has the form \((px + q)^{2} = p^{2}x^{2} + 2pqx + q^{2}\). Compare this with \(9x^{2} + 12x + 4\):

• \(p^{2} = 9\) implies \(p = 3\).
• \(q^{2} = 4\) implies \(q = 2\).
• \(2pq = 2 \cdot 3 \cdot 2 = 12\), which matches the middle term.

Write the factored form

Since the expression matches the perfect square trinomial form, it can be factored as \((3x + 2)^{2}\).

The factored form of \(9x^{2} + 12x + 4\) is \(\boxed{(3x + 2)^{2}}\).

The factored form of \(9x^{2} + 12x + 4\) is \(\boxed{(3x + 2)^{2}}\).
The correct answer is b.