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

User Visus Zhao
by
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1 Answer

11 votes

Answer:

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
User Pranphy
by
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