What is the factored form of the expression 8x² + 12x?

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To factor the expression 8x² + 12x, we will follow a systematic approach. Here’s how you can do it:

  1. Identify the Greatest Common Factor (GCF): The first step in factoring is to find the GCF of the coefficients and the variable terms. In this case, the coefficients are 8 and 12. The GCF of 8 and 12 is 4. Additionally, both terms have an x in them, so we can also factor out x.
  2. Factor out the GCF: Now, we can factor out 4x from the expression. This gives us: 
    8x² + 12x = 4x(2x + 3)
  3. Write the factored form: Therefore, the factored form of the expression 8x² + 12x is:
    4. 4x(2x + 3)

To summarize, the factored form of 8x² + 12x is 4x(2x + 3). This factorization makes it easier to analyze the expression for roots or other purposes, while also helping in simplifying mathematical operations involving this polynomial.

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