SAT Math Multiple Choice Question 938: Answer and Explanation

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Question: 938

6. If x2 – 2x – 15 = (x + r)(x + s) for all values of x, what is one possible value of rs?

  • A. –3
  • B. –2
  • C. 2
  • D. 8

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Strategic Advice: Whenever you are given two expressions and told that they are equal, look for ways to manipulate one so that it resembles the other.

Getting to the Answer: Notice that the expressions on both sides of the equal sign are quadratics-one is written in factored form and the other in standard form. Begin by factoring the left side of the equation to make it look like the right side. The factors of -15 that add up to -2 are 3 and -5, so the factored form of the left side is (x + 3)(x - 5). Although you can't tell which constant represents r and which represents s, remember that the question asks for a possible value of r - s. The two possible differences are 3 - (-5) = 8 and -5 - 3 = -8. The first combination is a match for (D).

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