# SAT Math Multiple Choice Question 902: Answer and Explanation

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**Question: 902**

**2.** If *g*(*x*) = -2(*x*^{2} – 6*x* – 12) + 3(*k* – *x*) and *g*(*x*) is evenly divisible by *x*, then what is the value of *k*?

- A. -8
- B. -3
- C. 2
- D. 3

**Correct Answer:** A

**Explanation:**

**A**

**Difficulty:** Medium

**Category:** Passport to Advanced Math / Exponents

**Strategic Advice:** If a polynomial is evenly divisible by *x*, then *x* has to be a factor of the polynomial, which means that when simplified, every term must have an *x* in it. In other words, the polynomial cannot contain a constant term.

**Getting to the Answer:** Start by simplifying *g*(*x*). Be careful when distributing the -2:

To ensure that there is no constant term, set 3*k* + 24 equal to 0 and solve for *k*.

The correct answer is (A).