Algebra-2

To write the polynomial in standard form given the zeros (x = 0), (x = 6), (x = -1), (x = 9), and (x = 3), we can express the polynomial in its factored form based on these zeros.

Given Zeros:

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

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

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

4.Zero: (x = 9) corresponds to the factor (x - 9)

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

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = x(x - 6)(x + 1)(x - 9)(x - 3)

Step 1: Multiply the Factors

We'll multiply the factors step by step.

Step 1.1: Multiply (x - 6) and (x + 1)

Step 1.2: Multiply () and (x - 9)

Step 1.3: Multiply () and (x - 3)

Now, we multiply this result by (x - 3):

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