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The 26th question in the image reads:

**"Find the value of the polynomial \(P(x)\) if one of the zeros of the quadratic polynomial is \(x = -1\)"**

Let's solve this step by step.

### Step 1: General form of a quadratic polynomial
The general form of a quadratic polynomial is:

\[
P(x) = ax^2 + bx + c
\]

### Step 2: Given information
- One zero of the polynomial is \(x = -1\). This means that \(P(-1) = 0\), i.e., substituting \(x = -1\) into the polynomial should make the polynomial equal to zero.

Using this, we can substitute \(x = -1\) into the general form:

\[
a(-1)^2 + b(-1) + c = 0
\]

\[
a - b + c = 0
\]

### Step 3: Solve for \(b\) or \(c\)
This equation relates the coefficients of the polynomial. However, since we only know that one of the zeros is \(x = -1\), we do not have enough information about the specific form of the polynomial or other zeros.

To proceed, we would need one of the following pieces of additional information:
- The complete form of the quadratic polynomial (specific values for \(a\), \(b\), and \(c\)), or
- The second zero of the polynomial, or
- The sum or product of the zeros of the polynomial.

Could you provide more information on the form of the polynomial or additional clues to complete the solution? Feel free to ask for details or explanations!

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Here are 5 relative questions to consider:

1. What is the second zero of the quadratic polynomial?
2. Is the polynomial provided anywhere else in the set of questions?
3. Can you use the sum or product of the zeros to find the other coefficients?
4. What happens if you try another method, like factoring the polynomial?
5. How does knowing one zero help determine the polynomial's general shape?

**Tip:** If you know both zeros of a quadratic polynomial, you can quickly factor it into a product of linear terms like \( (x - \text{zero}_1)(x - \text{zero}_2) \).

Find the value of the polynomial P(x) if one of the zeros of the quadratic polynomial is x = -1.

Learn how to find the value of a quadratic polynomial when one of the zeros is known. This problem uses the general form of quadratic polynomials and the Factor Theorem, suitable for students in Grades 9-12.

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