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

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

Explanation:

You want the x-intercepts of the polynomial function (x -1)(x -4)(x +7).

X-intercepts

The x-intercepts are the values of x where the function value is zero. The zero product rule tells us that the product of factors will be zero only if one or more of the factors is zero. Here that means we can find the zeros of the function by finding the values of x that make the factors zero:

x -1 = 0 ⇒ x = 1

x -4 = 0 ⇒ x = 4

x +7= 0 ⇒ x = -7

The x-intercepts of the graph are (1, 0), (4, 0) and (-7, 0), choice C.

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