Question

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)

Answer 1

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 2

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

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.