# SAT Math Multiple Choice Question 939: Answer and Explanation

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**Question: 939**

**7.** If *k* is a positive integer less than 17, what is the total number of possible integersolutions for the equation *x*^{2} + 8*x* + *k* = 0?

- A. 5
- B. 6
- C. 7
- D. 8

**Correct Answer:** C

**Explanation:**

**C**

**Difficulty:** Hard

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

**Strategic Advice:** When a quadratic equation is factored, the value of the constant (here, *k*) is equal to the product of the two constants in the binomial factors. Determine how many combinations there are, and you'll have your answer.

**Getting to the Answer:** Imagine factoring the given equation: You would need to find the factors of *k* (which you're told is less than 17) that add up to 8. List all possible integer combinations whose sum is 8 and whose product is less than 17:

(*x* + 1)(*x* + 7) = 0: 2 solutions

(*x* + 2)(*x* + 6) = 0: 2 solutions

(*x* + 3)(*x* + 5) = 0: 2 solutions

(*x* + 4)(*x* + 4) = 0: 1 solution

There are 7 different integer solutions for this equation, which matches (C).