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A polynomial function can be written as (x 1)(x 4)(x − 7). what are the x-intercepts of the graph of this function? (1, 0), (4, 0), (7, 0) (−1, 0), (−4, 0), (−7, 0) (1, 0), (4, 0), (−7, 0) (−1, 0), (−4, 0), (7, 0)

Respuesta :

apologiabiology
easy

set to zero
those are the roots or xintersepts

(x+1)(x+4)(x-7)=0

x+1=0
x=-1

x+4=0
x=-4

x-7=0
x=7

xints are (-4,0) (-1,0) (7,0)

Answer:

Fourth option is correct. The x-intercepts of the given functions are (-1,0),(-4,0) and (7,0).

Step-by-step explanation:

The given polynomial function is

[tex]P(x)=(x+1)(x+4)(x-7)[/tex]

To find the x-intercepts of the graph of this function, equate the given function equal to zero.

[tex]P(x)=0[/tex]

[tex](x+1)(x+4)(x-7)=0[/tex]

Using zero product property, equate each factor equal to zero.

[tex]x+1=0\Rightarrow x=-1[/tex]

[tex]x+4=0\Rightarrow x=-4[/tex]

[tex]x-7=0\Rightarrow x=7[/tex]

Therefore the x-intercepts of the given functions are (-1,0),(-4,0) and (7,0). Fourth option is correct.

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