If -1 and 4 are both roots of a given polynomial, then which of the following must be a factor of the polynomial?

(A) x – 1

(B) x2 + 3x − 4

(B) x2 – 3x − 4

(D) x + 4

Solution:

Choice C is correct.

Since, -1 and 4 are both roots of a given polynomial.

Therefore, (x+1) and (x-4) must be factors of the given polynomial.

Hence, their product must also be a factor of given polynomial.

The product of the factors = (x+1)(x-4)

= x2 – 3x − 4