Algebra-2

To find the polynomial in standard form given the zeros x = -4, x = 0, and x = 5, we will start with the factored form and expand it.

 

Given Zeros:

1.(x = -4) corresponds to the factor (x + 4)

2.(x = 0) corresponds to the factor (x)

3.(x = 5) corresponds to the factor (x - 5)

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = (x + 4)(x)(x - 5)

 

Expanding the Polynomial:

First, expand (x + 4)(x):

 

Now multiply this result by (x - 5):

Distributing the terms: