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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)

Verified Answer :

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

\(P(x)=(x+1)(x+4)(x-7)\)

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

\(P(x)=0\)

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

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

\(x+1=0\Rightarrow x=-1\)

\(x+4=0\Rightarrow x=-4\)

\(x-7=0\Rightarrow x=7\)

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

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