Question

Write a polynomial function in standard form with given zero x=1,-2,-7

Answer 1

f(x) = x³ + 8x² + 5x - 14

General Formulas and Concepts:

Pre-Algebra

• Distributive Property

Algebra I

• Terms/Coefficients/Degrees
• Expand by FOIL (First Outside Inside Last)
• Binomial Roots

Explanation:

Step 1: Define

Zeros x = 1, -2, -7

Step 2: Find Polynomial

1. Rewrite zeros: f(x) = (x - 1)(x + 2)(x + 7)
2. Expand [FOIL]: f(x) = (x² + 2x - x - 2)(x + 7)
3. Combine like terms (x): f(x) = (x² + x - 2)(x + 7)
4. Expand [Distribute]: f(x) = x³ + x² - 2x + 7x² + 7x - 14
5. Combine like terms (x²): f(x) = x³ + 8x² - 2x + 7x - 14
6. Combine like terms (x): f(x) = x³ + 8x² + 5x - 14