Question

Which binomial is a common factor of the polynomials (x^2−13x−30) and (x^2−x−6)?

A) x−6
B) x+3
C) x+2
D) x−5

Answer 1

The common factor of the polynomials (x²−13x−30) and (x²−x−6) is the binomial x+2, making C) x+2 the correct option.

Step-by-step explanation:

The question asks us to find the binomial that is a common factor of the two given polynomials: (x2−13x−30) and (x2−x−6). To solve this, we should factor each polynomial to find the common factor.

1. Factor the first polynomial (x2−13x−30). The factors are (x+2)(x−15), since (x+2)(x−15) = x2 − 15x + 2x − 30 = x2 − 13x − 30.
2. Factor the second polynomial (x2−x−6). The factors are (x+2)(x−3), since (x+2)(x−3) = x2 − 3x + 2x − 6 = x2 − x − 6.
3. Identify the common factor between the two which is (x+2).

The binomial that is a common factor of both polynomials is x+2, therefore the correct option is C) x+2.