Question

Write the equation of the polynomial, as described.

Roots at x = 10, 5, -1
Rises left and falls right.

A) (x - 10)(x - 5)(x + 1)
B) (x + 10)(x + 5)(x - 1)
C) (x - 10)(x + 5)(x - 1)
D) (x + 10)(x - 5)(x + 1)

Answer 1

The equation of the polynomial with roots at x = 10, 5, -1 and that rises left and falls right is A) (x - 10)(x - 5)(x + 1), as it factors directly from the roots and has the correct end behavior.

Step-by-step explanation:

The correct answer to the question is A) (x - 10)(x - 5)(x + 1). This can be determined by recognizing that a polynomial equation is constructed from its roots by creating factors of the form (x - root). The given roots are x = 10, 5, -1, thus creating the factors (x - 10), (x - 5), and (x + 1). The resulting polynomial must also have a positive leading coefficient to ensure that the graph rises to the left and falls to the right, as this describes the end behavior of the function. Only option A matches the roots and the described end behavior.