Factor each trinomial, if possible. See Examples 3 and 4. 9m² -12m+4

Verified step by step guidance

1. Identify the trinomial to factor: \$9m^2 - 12m + 4$.
2. Check if the trinomial is a perfect square trinomial by comparing it to the form \(a^2 - 2ab + b^2\).
3. Calculate the square roots of the first and last terms: \(\sqrt{9m^2} = 3m\) and \(\sqrt{4} = 2\).
4. Verify if the middle term matches \(-2 \times 3m \times 2 = -12m\), which it does, confirming it is a perfect square trinomial.
5. Write the factored form as the square of a binomial: \((3m - 2)^2\).

Key Concepts

Factoring Trinomials

Factoring trinomials involves expressing a quadratic expression of the form ax^2 + bx + c as a product of two binomials. This process simplifies the expression and helps solve equations or analyze functions. Recognizing patterns and using methods like trial and error or the AC method are common approaches.

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial, typically in the form a^2 ± 2ab + b^2 = (a ± b)^2. Identifying this pattern allows for quick factoring without trial and error, as it represents a special case of factoring.

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest factor shared by all terms in an expression. Factoring out the GCF first simplifies the trinomial and makes further factoring easier. It is a crucial initial step before applying other factoring techniques.