Find the \( x \)-intercepts and \( y \)-intercept of the following function. \[ f(x)=(x-2)(x+2)(5 x+40) \] Write your answer in coordinate pairs of the form \( (x, y) \) Provide your answer below: \( x \)-intercept: \( (\square, \square) \) and \( (\square, \square), \square \)-intercept: \( \qquad \square, \square) \)

To find the \( x \)-intercepts, we set \( f(x) = 0 \): \[ (x-2)(x+2)(5x+40) = 0 \] Setting each factor to zero gives us: 1. \( x - 2 = 0 \) → \( x = 2 \) 2. \( x + 2 = 0 \) → \( x = -2 \) 3. \( 5x + 40 = 0 \) → \( 5x = -40 \) → \( x = -8 \) Thus, the \( x \)-intercepts are \( (2, 0) \), \( (-2, 0) \), and \( (-8, 0) \). Next, for the \( y \)-intercept, we set \( x = 0 \): \[ f(0) = (0-2)(0+2)(5(0)+40) = (-2)(2)(40) = -160 \] So, the \( y \)-intercept is \( (0, -160) \). Putting it all together: \( x \)-intercepts: \( (2, 0) \) and \( (-2, 0) \) and \( (-8, 0) \) \( y \)-intercept: \( (0, -160) \)