Question

Consider the following polynomial function.f(x) = (x + 2)²(x-4)³(x − 3)Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(sAnswerSelect the number of x-intercept(s) at which f crosses the axis.Selecting an option will display any text boxes needed to complete your answer.none023

Answer 1

Given

The polynomial function,

`f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)`

To find: The x-intercepts.

Step-by-step explanation:

It is given that,

`f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)`

That implies,

The x-intercept is determined by setting f(x)=0.

Then,

`\begin{gathered} f\mleft(x\mright)=0 \\ (x+2)²\left(x-4\right)³\left(x−3\right)=0 \\ (x+2)^2=0,\text{ }(x-4)^3=0,\text{ }x-3=0 \\ x+2=0,\text{ }x-4=0,\text{ }x-3=0 \\ x=-2,\text{ }x=4,\text{ }x=3. \end{gathered}`

Hence, the x-ntercepts are (-2,0), (4,0), (3,0).