Algebra-2

To write the polynomial in standard form given the zeros (x = -5), (x = 3) (with multiplicity 2), (x = 0), and (x = 1), we can express the polynomial in its factored form based on these zeros.

 

Given Zeros:

1.Zero: (x = -5) corresponds to the factor (x + 5)

2.Zero: (x = 3) (multiplicity 2) corresponds to the factor

3.Zero: (x = 0) corresponds to the factor (x)

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

 

Step 1: Expand

First, we expand :

 

Step 2: Multiply the Factors

Now, we substitute this back into the polynomial:

 

Step 3: First Multiply (x + 5) with

Next, we'll multiply (x + 5) with :

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