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