A polynomial function has roots - 5 and 1. Which of the following could represent this function? f (x) = (x + 5) (x + 1) f (x) = (x - 5) (x - 1) f (x) = (x - 5) (x + 1) f (x) = (x + 5) (x - 1)

f (x) = (x + 5) (x - 1)

using the ' factor theorem '

given x = a is the root of a polynomial then (x - a) is a factor

here roots are x = - 5 and x = 1 hence factors are (x + 5) and (x - 1)

the polynomial is the product of the factors

f (x) = (x + 5) (x - 1)

2nd part of the question: The corresponding polynomial function is:

F (X) = X^2+4X-5