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

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

Options:

  1. (x + 3)(x + 3)
  2. (x - 3)(x - 3)
  3. (x + 2)(x + 4)
  4. (x + 1)(x + 9)

Correct Answer: (x + 3)(x + 3)

Solution: 

The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.

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

Practice Questions

Q1
What is the factored form of x^2 + 6x + 9?
  1. (x + 3)(x + 3)
  2. (x - 3)(x - 3)
  3. (x + 2)(x + 4)
  4. (x + 1)(x + 9)

Questions & Step-by-Step Solutions

What is the factored form of x^2 + 6x + 9?
  • Step 1: Identify the expression you want to factor, which is x^2 + 6x + 9.
  • Step 2: Look for two numbers that multiply to the last term (9) and add up to the middle term (6).
  • Step 3: The numbers 3 and 3 work because 3 * 3 = 9 and 3 + 3 = 6.
  • Step 4: Rewrite the expression using these numbers: x^2 + 3x + 3x + 9.
  • Step 5: Group the terms: (x^2 + 3x) + (3x + 9).
  • Step 6: Factor out the common terms in each group: x(x + 3) + 3(x + 3).
  • Step 7: Now, you can factor out (x + 3): (x + 3)(x + 3).
  • Step 8: This can also be written as (x + 3)^2.
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