In Exercises 95–104, factor completely.0.04x² + 0.12x + 0.09

Verified step by step guidance

1. Step 1: Identify the common factor in the coefficients. Notice that 0.04, 0.12, and 0.09 are all divisible by 0.01.
2. Step 2: Factor out the common factor of 0.01 from the entire expression. This gives us 0.01(4x^2 + 12x + 9).
3. Step 3: Focus on factoring the quadratic expression inside the parentheses: 4x^2 + 12x + 9.
4. Step 4: Recognize that 4x^2 + 12x + 9 is a perfect square trinomial. It can be expressed as (2x + 3)^2.
5. Step 5: Combine the factored terms to express the original expression as 0.01(2x + 3)^2.

Key Concepts

Factoring Quadratic Expressions

Factoring quadratic expressions involves rewriting the expression in the form of a product of two binomials. This process is essential for simplifying equations and solving for variable values. The standard form of a quadratic is ax² + bx + c, and the goal is to express it as (px + q)(rx + s), where p, q, r, and s are constants.

Common Factor Extraction

Common factor extraction is the process of identifying and factoring out the greatest common factor (GCF) from all terms in an expression. This simplifies the expression and makes it easier to factor further. In the given quadratic, the GCF can be identified to simplify the coefficients before applying other factoring techniques.

Perfect Square Trinomials

A perfect square trinomial is a specific type of quadratic expression that can be factored into the square of a binomial. It takes the form a² + 2ab + b², which factors to (a + b)². Recognizing this pattern can simplify the factoring process, especially when the coefficients are perfect squares, as seen in the given expression.