which of the following describes the roots of the polynomial function (f(x)=(x + 2)^2(x - 4)(x + 1)^3)?\n-2…

Answer:

A. -2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3

Explanation:

Step1: Recall root - multiplicity concept

For a polynomial in factored form $(x - a)^n$, $a$ is a root and $n$ is its multiplicity.

Step2: Analyze $(x + 2)^2$

Set $x+2 = 0$, we get $x=-2$. The exponent 2 means -2 has multiplicity 2.

Step3: Analyze $(x - 4)$

Set $x - 4=0$, we get $x = 4$. The exponent 1 means 4 has multiplicity 1.

Step4: Analyze $(x + 1)^3$

Set $x+1 = 0$, we get $x=-1$. The exponent 3 means -1 has multiplicity 3.