Algebra-2

To find the polynomial in standard form given the zeros x = 0, x = 1, and x = -5, we will first write the polynomial in its factored form and then expand it.

 

Given Zeros:

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

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

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = (x)(x - 1)(x + 5)

 

Expanding the Polynomial:

First, multiply (x - 1)(x + 5):

 

Now multiply this result by (x):