Question

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

Answer 1

not really sure but maybe: 0=(x-3)(x+1)(x+7) and then simplify it?

Explanation:

y=(x-3)(x+1)(x+7)

=x^3+5x^2-17x-21

Answer 2

f(x) = x³ + 5x² - 17x - 21

General Formulas and Concepts:

Algebra I

• Standard Form: f(x) = axⁿ + bxⁿ⁻¹ + cx + d
• Roots of a Polynomial: (x + a)(x + b)(x + c)(x + ...)
• Expanding by FOIL-ing
• Combining Like Terms

Explanation:

Step 1: Define

Roots x = -7, -1, 3

Step 2: Find function

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