SAT Math Multiple Choice Question 912: Answer and Explanation
If p(x) is the polynomial function shown in the graph above, which of the following couldbe the factored form of p(x)?
Correct Answer: D
Category: Passport to Advanced Math / Functions
Strategic Advice: The graph of a polynomial function crosses the x-axis when there is a single root and just touches the x-axis when there is a double root. A double root occurs when a factor is repeated, or in other words, is raised to the second power. For example, the factor (x - a) produces a single root at x = a, while (x - b)2 produces a double root at x = b.
Getting to the Answer: Examine the graph. The function crosses the x-axis at x = -4, which means one factor is (x - (-4)), or (x + 4). This means you can eliminate A and B. The function just touches the x-axis at x = 3, which means the other factor (which should be raised to the second power) is (x - 3). The factored form of the polynomial could be p(x) = (x + 4)(x - 3)2, which is (D).