Final answer:
To factor the trinomial 8x^2 + 24x + 12 by finding the GCF, we factor out the GCF of the coefficients and then factor the quadratic expression using the quadratic formula. The factored form is 4(2x - 3 + √3)(x - 3 - √3).
Step-by-step explanation:
To factor the trinomial 8x2 + 24x + 12 by finding the Greatest Common Factor (GCF), we need to find the largest number that can divide evenly into each term. First, let's factor out the GCF of the coefficients, which is 4. This gives us 4(2x2 + 6x + 3). Now let's factor the quadratic expression within the parentheses. To do this, we can use the quadratic formula, factoring by grouping, or trial and error. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = 6, and c = 3. Plugging these values into the quadratic formula, we get:
- x = (-6 ± √(6^2 - 4(2)(3))) / (2(2))
- x = (-6 ± √(36 - 24)) / 4
- x = (-6 ± √12) / 4
- x = (-6 ± 2√3) / 4
- x = (-3 ± √3) / 2
So our factored form is 4(2x - 3 + √3)(x - 3 - √3).
Learn more about Factoring Trinomials