Question

Question 18(Multiple Choice Worth 5 points)

(09.07 MC)
Given a polynomial f(x), if (x - 1) is a factor, what else must be true?

A. f(0) = 1
b. f(1) = 0
c. f(-1) = 0
d. (0) = -1

Answer 1

Answer: Option b

`f (1) = 0`

Explanation:

For a function of the form

`f (x) = ax ^ n + bx ^ {n-1} + ... + c`

Where n is the main exponent of the polynomial and a, b c are the coefficients of the variables then this polynomial can be written based on its factors as

`f (x) = a (x-h) (x-k) (x-s)...`

Where
`x = h`,
`x = k`,
`x = s`, ... are the points where
`f(x) = 0`

Therefore if for this case we know that

`(x-1)` is a factor of a polynomial function
`f (x)` then it is fulfilled that

`f (1) = 0`