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Factor the expression 3x^2 - 12.

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Question: Factor the expression 3x^2 - 12.

Options:

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

Correct Answer: 3(x^2 - 4)

Solution: 

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).

Factor the expression 3x^2 - 12.

Practice Questions

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

Questions & Step-by-Step Solutions

Factor the expression 3x^2 - 12.
  • Step 1: Look at the expression 3x^2 - 12.
  • Step 2: Identify the greatest common factor (GCF) of the terms. The GCF of 3x^2 and -12 is 3.
  • Step 3: Factor out the GCF (3) from the expression. This gives us 3(x^2 - 4).
  • Step 4: Now, look at the expression inside the parentheses: x^2 - 4.
  • Step 5: Recognize that x^2 - 4 is a difference of squares, which can be factored as (x - 2)(x + 2).
  • Step 6: Substitute back the factored form into the expression. So, we have 3(x - 2)(x + 2).
  • Step 7: The complete factorization of the original expression 3x^2 - 12 is 3(x - 2)(x + 2).
  • Factoring Quadratic Expressions – The process of breaking down a quadratic expression into its simplest components, often involving finding the greatest common factor and recognizing patterns such as the difference of squares.
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