Finding the zeros of a polynomial involves determining the values of the variable that make the polynomial equal to zero. Here's a step-by-step guide, assuming the polynomial is already factored:
Steps to Find Zeros of a Factored Polynomial
The following steps will guide you through the process of finding the zeros of a polynomial when it is in factored form, based on the provided reference.
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Set Each Factor Equal to Zero: Take the first factor of your polynomial and set it equal to zero.
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Solve for the Variable: Solve the equation you created in Step 1 to find the value of the variable. This value is a zero of the polynomial.
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Repeat for All Factors: Continue setting each of the remaining factors equal to zero and solving for the variable until you have done this for all factors in the factored form of the polynomial.
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List All Zeros: Once you've solved for all factors, list all the values you found for the variable. These are the zeros of the polynomial.
Example
Let's say you have the polynomial: (x - 2)(x + 1)(x - 5) = 0
Here's how you would find the zeros:
| Step | Action | Result |
|---|---|---|
| 1 | Set (x - 2) equal to zero | x - 2 = 0 |
| 2 | Solve for x | x = 2 |
| 3 | Set (x + 1) equal to zero | x + 1 = 0 |
| 4 | Solve for x | x = -1 |
| 5 | Set (x - 5) equal to zero | x - 5 = 0 |
| 6 | Solve for x | x = 5 |
| 7 | List all zeros | x = 2, -1, 5 |
Therefore, the zeros of the polynomial (x - 2)(x + 1)(x - 5) are 2, -1, and 5.
