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The equation x^2 + 2x + 1 = 0 can be factored as:

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Question: The equation x^2 + 2x + 1 = 0 can be factored as:

Options:

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

Correct Answer: (x + 1)(x + 1)

Solution: 

This is a perfect square: (x + 1)^2 = 0.

The equation x^2 + 2x + 1 = 0 can be factored as:

Practice Questions

Q1
The equation x^2 + 2x + 1 = 0 can be factored as:
  1. (x + 1)(x + 1)
  2. (x - 1)(x - 1)
  3. (x + 2)(x + 1)
  4. (x - 2)(x - 1)

Questions & Step-by-Step Solutions

The equation x^2 + 2x + 1 = 0 can be factored as:
  • Step 1: Look at the equation x^2 + 2x + 1 = 0.
  • Step 2: Identify the coefficients: The coefficient of x^2 is 1, the coefficient of x is 2, and the constant term is 1.
  • Step 3: Notice that the equation can be rewritten as (x + 1)(x + 1) = 0.
  • Step 4: Recognize that (x + 1)(x + 1) is the same as (x + 1)^2.
  • Step 5: Therefore, we can say (x + 1)^2 = 0.
  • Factoring Quadratic Equations – Understanding how to factor quadratic equations, particularly recognizing perfect squares.
  • Perfect Square Trinomials – Identifying and applying the formula for perfect square trinomials, which is (a + b)^2 = a^2 + 2ab + b^2.
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