What is the factored form of the expression x^2 - 6x + 9?

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Question: What is the factored form of the expression x^2 - 6x + 9?

Options:

Correct Answer: (x - 3)(x - 3)

Solution:

This is a perfect square trinomial. The factored form is (x - 3)(x - 3) or (x - 3)^2.

What is the factored form of the expression x^2 - 6x + 9?

What is the factored form of the expression x^2 - 6x + 9?

Step 1: Identify the expression you want to factor, which is x^2 - 6x + 9.
Step 2: Look for a perfect square trinomial. A perfect square trinomial has the form (a - b)^2 = a^2 - 2ab + b^2.
Step 3: In the expression x^2 - 6x + 9, notice that x^2 is a perfect square (a^2) and 9 is also a perfect square (b^2), since 3^2 = 9.
Step 4: Find the middle term. The middle term is -6x. This can be written as -2ab, where a = x and b = 3.
Step 5: Check if -2ab equals -6x. Since -2(x)(3) = -6x, it matches.
Step 6: Since the expression fits the perfect square trinomial form, we can write it as (x - 3)(x - 3).
Step 7: This can also be written in a simpler form as (x - 3)^2.

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