Question

find the zeros of the function g(x). g(x) = (x + 1)²(x - 2)(x + 2) write your answer as a list of values separated by commas. x =

Explanation:

Step1: Set \( g(x) = 0 \)

We know that to find the zeros of a function \( g(x) \), we set \( g(x)=0 \). So we have the equation \((x + 1)^2(x - 2)(x + 2)=0\).

Step2: Apply zero - product property

The zero - product property states that if \( ab = 0\), then either \( a = 0\) or \( b = 0\) (or both). For the equation \((x + 1)^2(x - 2)(x + 2)=0\), we set each factor equal to zero:

• For the factor \((x + 1)^2\): Set \((x + 1)^2=0\). Taking the square root of both sides, we get \(x+1 = 0\), so \(x=-1\). Since the exponent of \((x + 1)\) is 2, the zero \(x = - 1\) has a multiplicity of 2, but we still list it as a zero of the function.
• For the factor \((x - 2)\): Set \(x - 2=0\), then \(x = 2\).
• For the factor \((x + 2)\): Set \(x+2 = 0\), then \(x=-2\).

Answer:

-1, 2, -2