Algebra-2

To write the polynomial in standard form given the zeros (x = 10), (x = -1), (x = 4), and (x = 0), we first express the polynomial in its factored form based on these zeros.

 

Given Zeros:

1.Zero: (x = 10) corresponds to the factor (x - 10)

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

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

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = x(x - 10)(x + 1)(x - 4)

 

Step 1: Multiply the Factors

First, we'll multiply (x - 10), (x + 1), and (x - 4).

 

Multiply (x - 10) and (x + 1):

 

Now multiply the result by (x - 4):

Using the distributive property:

 

Combining like terms:

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