Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure.
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Question

Quizplus · Accepted Answer

The x-intercepts are at (−5,0), (−2,0), and (4,0), so the factors of the polynomial include:
(x+5)(x+2)(x-4)
Since the degree of the polynomial is not specified, the lowest possible degree polynomial is a cubic (degree 3). Thus, we need to include one more factor of (x-a), where a is another x-intercept. From the graph, we can see that there is only one real root, which is at x=1. Therefore, the polynomial is:
f(x) = (x+5)(x+2)(x-4)(x-1)

Expanding this out gives:
f(x) = x^4 + 2x^3 - 10x^2 - 28x + 40

C) 11ebb6d7_48e5_68e7_b437_41e0a817d149_TB8593_11

Write an Equation for the Lowest-Degree Polynomial Function with the Graph