Question

Write a polynomial function in standard form with zeros at -4, 1, 1

Answer 1

The polynomial has zeros at -4,1,1, therefore its factors are
(x+4), (x-1)²
The polynomial is of the form
f(x) = a(x+4)(x-1)²
      = a(x+4)(x² - 2x + 1)
      = a(x³ - 2x² + x + 4x² - 8x + 4)
      = a(x³ + 2x² - 7x + 4) 

a is an arbitrary constant. By setting it equal to  1, a polynomial in standard form is
f(x) = x³ + 2x² - 7x + 4

Answer: f(x) = x³ + 2x² - 7x + 4