2
advanced-math

Find the x-intercepts of y=(x3)(x+2)y = (x - 3)(x + 2).

A

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

B

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

C

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

D

(3,2)(3, -2)

Correct Answer: A

Choice A is the correct answer. The x-intercepts are found by setting y=0y = 0.

  1. Set (x3)(x+2)=0(x - 3)(x + 2) = 0.
  2. Apply Zero Product Property:
    • x3=0x=3x - 3 = 0 \Rightarrow x = 3
    • x+2=0x=2x + 2 = 0 \Rightarrow x = -2
  3. The coordinates are (3,0)(3, 0) and (2,0)(-2, 0).

Choice B is incorrect because of sign errors (common mistake). Choice C is incorrect because it lists them as y-intercepts. Choice D is incorrect because it combines them into one point.