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

f(x) = x³ + 8x² + 5x - 14

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Terms/Coefficients/DegreesExpand by FOIL (First Outside Inside Last)Binomial Roots

Step-by-step explanation:

Step 1: Define

Zeros x = 1, -2, -7

Step 2: Find Polynomial

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