Algebra-2

To write the polynomial in standard form given the zeros (x = 6), (x = -2) (with multiplicity 2), and (x = -4), we first express the polynomial in its factored form and then expand it.

 

Given Zeros:

1.Zero: (x = 6) corresponds to the factor (x - 6)

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

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

 

Step 1: Expand

First, we expand :

 

Step 2: Multiply by (x + 4)

Now we multiply by (x + 4):

 

Using the distributive property:

 

Step 3: Multiply by (x - 6)

Now we multiply the result by (x - 6):

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