Mathematics ACT Aspire Test 2025 – 400 Free Practice Questions to Pass the Exam

A perfect square trinomial is a specific type of polynomial that can be expressed as the square of a binomial. The general form of a perfect square trinomial is \( (a + b)² = a² + 2ab + b² \) or \( (a - b)² = a² - 2ab + b² \).

In the case of the trinomial \( x² + 4x + 4 \), we can analyze its components:

- The first term \( x² \) represents \( a² \).

- The last term \( 4 \) can be rewritten as \( 2² \), which indicates \( b² \) where \( b = 2 \).

- The middle term \( 4x \) can be represented as \( 2ab \). If we substitute \( a = x \) and \( b = 2 \), we find that \( 2ab = 2(x)(2) = 4x \).

Since it fits the format \( (x + 2)² \), this confirms that \( x² + 4x + 4 \) is indeed a perfect square trinomial.

In contrast, the other trinomials