SAT Math Multiple Choice Question 902: Answer and Explanation
2. If g(x) = -2(x2 – 6x – 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
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 3k + 24 equal to 0 and solve for k.
The correct answer is (A).