Question

A polynomial function can be written as (x + 2)(x + 3)(x − 5). What are the x-intercepts of the graph of this function? (1 point) (2, 0), (3, 0), (−5, 0) (−2, 0), (−3, 0), (5, 0) (2, 0), (3, 0), (5, 0) (−2, 0), (−3, 0), (−5, 0)

Answer 1

(-2, 0), (-3, 0) and (5, 0)

Explanation:

x-intercepts are for

(x + 2)(x + 3)(x - 5) = 0

The product is equal to 0 if one of the factors is equal to 0.

Therefore

x + 2 = 0 or x + 3 = 0 or x - 5 = 9

x + 2 = 0 subtract 2 from both sides

x = -2

x + 3 = 0 subtract 3 from both sides

x = -3

x - 5 = 0 add 5 to both sides

x = 5

Answer 2

(-2, 0), (-3, 0), and (5, 0)

Explanation:

The x-intercept is found when y = 0.

So, we have to find x when (x + 2)(x + 3)(x - 5) = 0

We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).

1. When x + 2 = 0, x = -2

2. When x + 3 = 0, x = -3

3. When x - 5 = 0, x = 5

That gives us (-2, 0), (-3, 0), and (5, 0)