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Select the correct answer.
Find the factors of function f.
f(x) = x^4 – 5x^3 – 4x^2 + 20x
Based on the factors, which statement is true about the graph of function f?

Α. The graph crosses the x-axis at the point (-5,0).
B. The graph crosses the x-axis at the point (-4,0).
C. The graph crosses the x-axis at the point (4,0).
D. The graph crosses the x-axis at the point (2,0).

Select the correct answer Find the factors of function f fx x4 5x3 4x2 20x Based on the factors which statement is true about the graph of function f Α The grap class=

Respuesta :

MrRoyal

The true statement about the factors of the function f is (d) The graph crosses the x-axis at the point (2,0).

The function is given as:

[tex]\mathbf{f(x) = x^4 - 5x^3 - 4x^2 + 20x}[/tex]

Factorize

[tex]\mathbf{f(x) = x^3(x - 5) - 4x(x - 5)}[/tex]

Factor out x - 5

[tex]\mathbf{f(x) = (x^3 - 4x) (x - 5)}[/tex]

Factor out x

[tex]\mathbf{f(x) = x(x^2 - 4) (x - 5)}[/tex]

Express 4 as 2^2

[tex]\mathbf{f(x) = x(x^2 - 2^2) (x - 5)}[/tex]

Apply the difference of two squares

[tex]\mathbf{f(x) = x(x - 2)(x + 2) (x - 5)}[/tex]

The above factorized expression means that, f(x) passes through the x-axis at x = 0, 2, -2 and 5

Hence, the true statement is (d)

Read more about factors at:

https://brainly.com/question/12827277

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