# SAT Math Multiple Choice Question 230: Answer and Explanation

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**Question: 230**

**5.** If the third degree polynomial x^{3} - 10x^{2} + 12x + 72 can be factored to (x + 2) · y^{2}, 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)y^{2} to get (x + 2)(x - 6)(x - 6). Multiply the last two factors together to get (x + 2)(x^{2} - 12x + 36). Multiply the two resulting factors together to get x^{3} - 12x^{2} + 36x + 2x^{2} - 24x + 72. Combine like terms to get x^{3} - 10x^{2} + 12x + 72. This is the same as the third degree polynomial in the question. Therefore, the correct answer is (A).