Questions: Consider the following polynomial function. f(x)=(x+3)(x-2)^2 Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(s).

Solution Steps

To find the x-intercepts of the polynomial function \( f(x) = (x+3)(x-2)^2 \), we need to determine the values of \( x \) for which \( f(x) = 0 \). This involves solving the equation \( (x+3)(x-2)^2 = 0 \). The solutions to this equation will give us the x-intercepts.

1. Set the polynomial function equal to zero: \( (x+3)(x-2)^2 = 0 \).
2. Solve for \( x \) by setting each factor equal to zero: \( x+3 = 0 \) and \( (x-2)^2 = 0 \).
3. Find the values of \( x \) that satisfy these equations.
4. Express the x-intercepts as ordered pairs.

To find the x-intercepts of the polynomial function \( f(x) = (x + 3)(x - 2)^2 \), we set the function equal to zero: \[ f(x) = 0 \implies (x + 3)(x - 2)^2 = 0 \]

We solve for \( x \) by setting each factor equal to zero:

1. \( x + 3 = 0 \) gives \( x = -3 \).
2. \( (x - 2)^2 = 0 \) gives \( x = 2 \).

The x-intercepts can be expressed as ordered pairs, where the y-coordinate is zero:

• For \( x = -3 \), the ordered pair is \( (-3, 0) \).
• For \( x = 2 \), the ordered pair is \( (2, 0) \).

Final Answer