Which of the following is the correct factorization of the polynomial below?2x2 - 12x + 18A.2(x - 3)2B.2(x + 6)(x + 3)C.(2x + 6)(x + 3)D.The polynomial is irreducible.
Question
Which of the following is the correct factorization of the polynomial below?2x2 - 12x + 18A.2(x - 3)2B.2(x + 6)(x + 3)C.(2x + 6)(x + 3)D.The polynomial is irreducible.
Solution
The correct factorization of the polynomial 2x^2 - 12x + 18 is A. 2(x - 3)^2.
Here's the step-by-step process:
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First, we can factor out a 2 from each term to simplify the polynomial: 2(x^2 - 6x + 9).
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Then, we can recognize that the expression inside the parentheses is a perfect square trinomial, which can be factored as (x - 3)^2.
So, the factorization of the polynomial 2x^2 - 12x + 18 is 2(x - 3)^2.
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