# SAT Math Multiple Choice Question 615: Answer and Explanation

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**Question: 615**

**15.** The function *g*(*x*) = *ax*^{3} + *bx*^{2} + *cx* + *d* has zeroes at *x* = -2, *x* = 3, and *x* = 6. If *g*(0) < 0, which of the following must also be negative?

- A.
*g*(-3) - B.
*g*(-1) - C.
*g*(4) - D.
*g*(5)

**Correct Answer:** B

**Explanation:**

**B**

**Advanced Mathematics (analyzing polynomial functions) HARD**

Because this polynomial has a degree of 3 (which is the highest power of any of its terms), it cannot have more than 3 zeros. These three zeros are given as -2, 3, and 6. We also know that *g*(0), the *y*-intercept of the graph, is negative. This gives us enough information to make a rough sketch of the graph.

This shows that the only values of *x* for which the function is negative are -2 < *x* < 3 and *x* > 6. Therefore the only negative value among the choices is (B) *g*(-1).