SAT Math Multiple Choice Question 921: Answer and Explanation

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Question: 921

5. The polynomial function p is defined by p(x) = 4x3 + bx2 + 41x + 12, where b is a constant. When graphed on a standard coordinate plane, p intersects the x-axis at (–0.25, 0), (3, 0), and (k, 0). What is the value of b?

  • A. –27
  • B.
  • C. 4
  • D. 27

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: A function's solutions are the point or points at which its graph crosses the x-axis. You're given two x-intercepts (two solutions), which you can use to find the value of b.

Getting to the Answer: The solution (3, 0) is the simplest of the intercepts given, so plug in 3 for each x and 0 for p(x), and solve for b:

(A) is the correct answer.

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