If p(x) is the polynomial functions shown in the graph above, which of the following could be fractored form of p(x)?

Options

A. `p(x)=(x-4)(x+3)`
B. `p(x)=(x-4)(x+3)^(2)`
C. `p(x)=(x+4)(x-3)`
D. `p(x)=(x+4)(x-3)^(2)`

Answer

D

Explanation

Difficult:Easy
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 roots occurs when a factor is repreated, or in other word, is raised to the second power. For example, the factor (x-a) produces a single root at x=a,while `(x-a)^(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 seconnd power) is x-3. The factored form of the polynomial could be `p(x)=(x+4)(x-3)^(2)`, which is (D).