SAT Math Multiple Choice Question 230: Answer and Explanation

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Question: 230

5. If the third degree polynomial x3 - 10x2 + 12x + 72 can be factored to (x + 2) · y2, what is y in terms of x ?

  • A. x - 6
  • B. x - 3
  • C. x - 1
  • D. x + 1

Correct Answer: A

Explanation:

A Given that all of the answer choices are possible values for y, plug in the answers. In (A), y = x - 6. Plug this value into (x + 2)y2 to get (x + 2)(x - 6)(x - 6). Multiply the last two factors together to get (x + 2)(x2 - 12x + 36). Multiply the two resulting factors together to get x3 - 12x2 + 36x + 2x2 - 24x + 72. Combine like terms to get x3 - 10x2 + 12x + 72. This is the same as the third degree polynomial in the question. Therefore, the correct answer is (A).

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