Question

Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2? a. f(x) = –x² – 8x – 16 b. f(x) = –x² + 8x – 16 c. f(x) = –x² – 8x + 16 d. f(x) = –x² + 8x + 16

Answer 1

b

Explanation:

given a degree 2 polynomial , that is a quadratic polynomial

given a polynomial with root x = 4 , then the factor is (x - 4)

given it is of multiplicity 2 then factor is (x - 4)²

with leading coefficient of - 1

Then

f(x) = - (x - 4)² ← expand using FOIL

f(x) = - (x² - 8x + 16) ← distribute parenthesis by - 1

f(x) = - x² + 8x - 16 ← (b)