Given
The polynomial function,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]To find: The x-intercepts.
Explanation:
It is given that,
[tex]f\mleft(x\mright)=(x+2)²\left(x-4\right)³\left(x−3\right)[/tex]That implies,
The x-intercept is determined by setting f(x)=0.
Then,
[tex]\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}[/tex]Hence, the x-ntercepts are (-2,0), (4,0), (3,0).
