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Select one of the factors of 3x^2 + 4x−4. A. (x + 4) B. (3x + 2) C. (3x − 2) D. (x − 2)
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Factor the given quadratic expression 3x^{2} + 4x - 4

Step 3:
: To factor this quadratic, we'll use the ac-method:

- First, multiply the coefficient of $$x^{2}$$ (3) by the constant term (-4)
- 3 \times (- 4) = - 12

Step 4:
: Find two numbers that:

- Multiply to give - 12 - Add to give the middle term's coefficient (4)

Step 5:
: By trial and error, we find that 6 and - 2 work:

- $$6 \times (-2) = -12
- 6 + (- 2) = 4

Step 6:
: Rewrite the middle term using these numbers:

3x^{2} + 6x - 2x - 4

Step 7:
: Group the terms:

(3x^{2} + 6x) + (-2x - 4)

Step 8:
: Factor out common terms from each group:

3x(x + 2) - 2(x + 2)

Step 9:
: Recognize the common factor (x + 2):

(3x - 2)(x + 2)

Step 10:
: Compare with the given options.

The factor (x + 2) appears in the factorization.

Final Answer

B. (3x + 2)