QQuestionMathematics
QuestionMathematics
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)
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