Algebra-2

To write the polynomial in standard form given the zeros (x = 0), (x = 2), (x = -5), (x = 3), and (x = 1), 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 = 2) corresponds to the factor (x - 2)

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

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

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

 

Polynomial in Factored Form:

The polynomial can be expressed as:

f(x) = x(x - 2)(x + 5)(x - 3)(x - 1)

 

Step 1: Multiply the Factors

We'll multiply the factors step by step.

Step 1.1: Multiply (x - 2) and (x + 5)

 

Step 1.2: Multiply the result with (x - 3)

 

Step 1.3: Multiply the result with (x - 1)

Now we multiply this result by (x - 1):