Question

22 consider a polynomial function whose equation is: $f(x)=x(x-2)^2(x+1)$
(a) part a
what degree is the function?

part b
classify the degree of the function as even or odd.

part c
describe the end behavior (select two!).
(b)
a $as\\ x \to +\infty, f(x) \to +\infty$
b $as\\ x \to +\infty, f(x) \to -\infty$
c $as\\ x \to -\infty, f(x) \to -\infty$
d $as\\ x \to -\infty, f(x) \to +\infty$

Explanation:

Step1: Find polynomial degree

Add exponents of factors: $1 + 2 + 1 = 4$

Step2: Classify degree parity

4 is divisible by 2, so even.

Step3: Analyze end behavior

Leading term is $x^4$ (positive coefficient, even degree):

• As $x \to +\infty$, $f(x) \to +\infty$
• As $x \to -\infty$, $f(x) \to +\infty$

Answer:

Part A: 4
Part B: Even
Part C: A. As $x \to +\infty$, $f(x) \to +\infty$, D. As $x \to -\infty$, $f(x) \to +\infty$