X=3,-1,-7 write a polynomial function in standard form with given zero

f(x) = x³ + 5x² - 17x - 21

General Formulas and Concepts:

Algebra I

Standard Form: f(x) = axⁿ + bxⁿ⁻¹ + cx + dRoots of a Polynomial: (x + a)(x + b)(x + c)(x + ...)Expanding by FOIL-ingCombining Like Terms

Step-by-step explanation:

Step 1: Define

Roots x = -7, -1, 3

Step 2: Find function

Write binomial roots:                    f(x) = (x - 3)(x + 1)(x + 7)Expand:                                         f(x) = (x² + x - 3x - 3)(x + 7)Combine like terms(x):                 f(x) = (x² - 2x - 3)(x + 7)Expand:                                         f(x) = x³ - 2x² - 3x + 7x² - 14x - 21Combine like terms(x²):                f(x) = x³ + 5x² - 3x - 14x - 21Combine like terms(x):                 f(x) = x³ + 5x² - 17x - 21