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Factor the expression x^2 + 4x - 12.

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Question: Factor the expression x^2 + 4x - 12.

Options:

  1. (x + 6)(x - 2)
  2. (x - 6)(x + 2)
  3. (x + 12)(x - 1)
  4. (x - 4)(x + 3)

Correct Answer: (x + 6)(x - 2)

Solution: 

We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).

Factor the expression x^2 + 4x - 12.

Practice Questions

Q1
Factor the expression x^2 + 4x - 12.
  1. (x + 6)(x - 2)
  2. (x - 6)(x + 2)
  3. (x + 12)(x - 1)
  4. (x - 4)(x + 3)

Questions & Step-by-Step Solutions

Factor the expression x^2 + 4x - 12.
  • Step 1: Identify the expression you want to factor, which is x^2 + 4x - 12.
  • Step 2: Look for two numbers that multiply to -12 (the constant term) and add to 4 (the coefficient of x).
  • Step 3: List the pairs of numbers that multiply to -12: (1, -12), (-1, 12), (2, -6), (-2, 6), (3, -4), (-3, 4).
  • Step 4: Check which pair adds up to 4. The pair (6, -2) works because 6 + (-2) = 4.
  • Step 5: Write the factored form using the numbers found: (x + 6)(x - 2).
  • Factoring Quadratic Expressions – The process of rewriting a quadratic expression in the form of a product of two binomials.
  • Finding Factors – Identifying two numbers that multiply to the constant term and add to the coefficient of the linear term.
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