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Which of the following is the correct factorization of the quadratic expression

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Question: Which of the following is the correct factorization of the quadratic expression x^2 - 5x + 6?

Options:

  1. (x - 2)(x - 3)
  2. (x + 2)(x + 3)
  3. (x - 1)(x - 6)
  4. (x + 1)(x + 6)

Correct Answer: (x - 2)(x - 3)

Solution: 

The expression factors to (x - 2)(x - 3) since -2 and -3 are the roots.

Which of the following is the correct factorization of the quadratic expression

Practice Questions

Q1
Which of the following is the correct factorization of the quadratic expression x^2 - 5x + 6?
  1. (x - 2)(x - 3)
  2. (x + 2)(x + 3)
  3. (x - 1)(x - 6)
  4. (x + 1)(x + 6)

Questions & Step-by-Step Solutions

Which of the following is the correct factorization of the quadratic expression x^2 - 5x + 6?
  • Step 1: Identify the quadratic expression, which is x^2 - 5x + 6.
  • Step 2: Look for two numbers that multiply to the constant term (6) and add up to the coefficient of the x term (-5).
  • Step 3: The two numbers that work are -2 and -3 because -2 * -3 = 6 and -2 + -3 = -5.
  • Step 4: Write the factors using these two numbers: (x - 2)(x - 3).
  • Step 5: Check your work by expanding (x - 2)(x - 3) to see if it equals the original expression.
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