Factor the expression 4x² - 12x + 9.

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Question: Factor the expression 4x² - 12x + 9.

Options:

Correct Answer: (2x - 3)²

Solution:

4x² - 12x + 9 = (2x - 3)².

Factor the expression 4x² - 12x + 9.

Factor the expression 4x² - 12x + 9.

Step 1: Identify the expression you want to factor: 4x² - 12x + 9.
Step 2: Look for a common factor in the first term (4x²), the second term (-12x), and the last term (9).
Step 3: Notice that 4 is a perfect square (2²) and 9 is also a perfect square (3²).
Step 4: Rewrite the expression in a form that resembles a perfect square trinomial: (2x)² - 2 * (2x) * (3) + (3)².
Step 5: Recognize that the expression can be factored as (2x - 3)².
Step 6: Write the final factored form: 4x² - 12x + 9 = (2x - 3)².

Factoring Quadratic Expressions – The process of rewriting a quadratic expression in the form of a product of its factors.
Perfect Square Trinomials – Recognizing and factoring expressions that can be expressed as the square of a binomial.