Question

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)

Answer 1

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

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

Explanation:

Answer 2

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)