Apolynomial function can be written as (x − 1)(x − 4)(x + 7). what are the x-intercepts of the graph of this function?
a (1, 0), (4, 0), (7, 0)
b (−1, 0), (−4, 0), (−7, 0)
c(1, 0), (4, 0), (−7, 0)
d (−1, 0), (−4, 0), (7, 0)

Option c is correct

(1, 0), (4, 0) and (-7, 0)

Step-by-step explanation:

x-intercepts states that the line cut the x-axis.

Substitute y = 0 and solve for x.

As per the statement:

A polynomial function can be written as (x − 1)(x − 4)(x + 7).

⇒y = (x − 1)(x − 4)(x + 7)

By definition of x-intercept:

Substitute y =0 we have;

By zero product property we have;

x-1 =0 , x-4 = 0 and x+7  =0

⇒x = 1, x = 4 and x = -7

⇒x-intercepts = (1, 0), (4, 0) and (-7, 0)

therefore, the x-intercepts of the graph of this function is, (1, 0), (4, 0) and (-7, 0)

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