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Factor the quadratic expression x^2 - 5x + 6.

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Question: Factor 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: 

To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

Factor the quadratic expression x^2 - 5x + 6.

Practice Questions

Q1
Factor 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

Factor the quadratic expression x^2 - 5x + 6.
  • Step 1: Identify the quadratic expression you want to factor, which is x^2 - 5x + 6.
  • Step 2: Look for two numbers that multiply to the constant term (6) and add 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 factored form using these two numbers: (x - 2)(x - 3).
  • Factoring Quadratics – The process of rewriting a quadratic expression in the form of a product of two binomials.
  • Finding Roots – Identifying two numbers that multiply to the constant term and add to the coefficient of the linear term.
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