Algebra-2

To write the polynomial in standard form given the zeros (x = 8), (x = -4) (with multiplicity 2), (x = 1), and (x = 5), we can express the polynomial in its factored form based on these zeros.

 

Given Zeros:

1.Zero: (x = 8) corresponds to the factor (x - 8)

2.Zero: (x = -4) (multiplicity 2) corresponds to the factor

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

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

 

Step 1: Expand

First, we expand :

 

Step 2: Substitute Back

Now we substitute this back into the polynomial:

 

Step 3: Multiply (x - 8) with

Next, we'll multiply (x - 8) with :

 

Step 4: Now Multiply by (x - 1)

Next, we multiply this result by (x - 1):

 

Using the distributive property: