1. Identify the degree, end behavior and roots (w (a) f(x) = r³(x + 1)²(x² + 9)(x² – 4) - (b) /(x) = 4z(27 - 9)"(2 - 2) (포 + 6)" %3D |

Degree of polynomial is the highest power of 'x' on polynomial equation

Roots are found when f(x) = 0 gives real vales of x for which f(x) = 0.

End behavior of polynomial is the value of f(x) when x tend to +/- infinity.

$$\begin{gathered} a\left) \\ f\right(x) = x^3{(x+1)}^2(x^2+9\left)\right(x^2-4) \\ \mathit{D}\mathit{e}\mathit{g}\mathit{r}\mathit{e}\mathit{e} \\ highest degree is found by adding \text{'}x\text{'} power of highest order. \\ f(x) = x^3(x^2+2x+1\left)\right(x^2+9\left)\right(x^2-4) \\ \text{'}x\text{'}highest power = 3+2+2+2 =9 = degree of f(x) \\ \mathit{E}\mathit{n}\mathit{d}\mathit{ }\mathit{b}\mathit{e}\mathit{h}\mathit{a}\mathit{v}\mathit{i}\mathit{o}\mathit{r} \\ \mathit{p}\mathit{u}\mathit{t}\mathbf{ }\mathit{x}\mathbf{\to }\mathbf{\infty } \\ f(x) \to \infty \\ \mathit{p}\mathit{u}\mathit{t}\mathbf{ }\mathit{x}\mathbf{\to }\mathbf{-}\mathbf{\infty } \\ f(x) \to -\infty \\ \mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{s} \\ \mathit{f}\mathit{(}\mathit{x}\mathit{)}\mathit{ }\mathit{=}\mathit{ }\mathit{0} \\ {\mathrm{x}}^3= 0 \Rightarrow \mathrm{x}=0, 0, 0 \\ \mathrm{or}, \mathrm{x}+1=0 \Rightarrow \mathrm{x}=-1 \\ \mathrm{or}, {\mathrm{x}}^2-4 = 0 \Rightarrow \mathrm{x}=+2 \mathrm{or} -2 \\ \mathrm{So}, \\ \mathrm{roots} = 0 , -1, 2 ,-2 \end{gathered}$$