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Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Respuesta :

Hagrid
Based on the given intercepts, the factors of the polynomial are
f(x) = (x-2)(x+1)(x-2)
Multiplying the binomials would give us the correct answer. Multiplying the first two,
f(x) = (x2 - x - 2)(x-2)
Then multiplying the result with other binomial,
f(x) = x3 + x2 - 4x - 4

Using the Factor Theorem, the function that best represents the graph is given by:

f(x) = x³ + x² - 4x - 4.

What is the Factor Theorem?

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient

In this problem, we consider a = 1, and the roots are the x-intercepts [tex]x_1 = -2, x_2 = -1, x_3 = 2[/tex], hence:

f(x) = (x + 2)(x + 1)(x - 2)

f(x) = (x² + 3x + 2)(x - 2)

f(x) = x³ + x² - 4x - 4.

More can be learned about the Factor Theorem at https://brainly.com/question/24380382

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