Algebra-2

To find the polynomial in standard form given the zeros x = 1, x = 2, and x = -2, we will start with the factored form of the polynomial and expand it.

 

Given Zeros:

1.(x = 1) corresponds to the factor (x - 1)

2.(x = 2) corresponds to the factor (x - 2)

3.(x = -2) corresponds to the factor (x + 2)

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = (x - 1)(x - 2)(x + 2)

 

Expanding the Polynomial:

First, multiply (x - 2)(x + 2):

 

Now multiply this result by (x - 1):

Distributing the terms: