Algebra-2

To write the polynomial in standard form given the zeros (x = -7), (x = 1), and (x = 3), we will first express the polynomial in factored form and then expand it.

 

Given Zeros:

1.Zero: (x = -7) corresponds to the factor (x + 7)

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

3.Zero: (x = 3) corresponds to the factor (x - 3)

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = (x + 7)(x - 1)(x - 3)

 

Expanding the Polynomial:

First, expand (x - 1)(x - 3):

 

Now, multiply this result by (x + 7):

Using the distributive property:

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