A polynomial function can be written as (x + 1)(x + 4)(x - 7). What are the x-intercepts of the graph of this function ?

The x-intercepts of this graph are -1, -4 and 7.
To find the x intercepts of a fully factored function like the one above, you simply have to set each parenthesis equal to 0 and solve for x. This will give you all of the x intercepts.
FIRST ONE
x + 1 = 0 ----> subtract 1
x = -1
SECOND ONE
x + 4 = 0 ----> subtact 4
x = -4
THIRD ONE
x - 7 = 0 ----> add 7
x = 7
Now you have all of your x intercepts.
D is the answer
x+1=0
Isolate x and you get -1
Next x+4=0
isolate x you get -4
Finally
x-7=0
isolate x and you get 7