Question

A polynomial function, f(x), has x-intercepts at (−6,0) and (2,0). What is one possible factor of f(x) in which the coefficient is 1?

A) (x + 6)
B) (x - 2)
C) (x + 2)
D) (x - 6)

Answer 1

The correct factor of the polynomial function f(x) with coefficient 1 that corresponds to the x-intercept (−6,0) is (x + 6).

Step-by-step explanation:

The (x + 6) because a polynomial function’s factors are related to its x-intercepts. An x-intercept at (2,0) means that x - 2 is a factor, and an x-intercept at (-6,0) means that x + 6 is a factor. Therefore, the factor with coefficient 1 associated with the x-intercept (-6,0) is (x + 6).

A polynomial function, f(x), has x-intercepts at (-6,0) and (2,0). To find one possible factor of f(x) in which the coefficient is 1, we can use the Zero Product Property. Since the x-intercepts are (-6,0) and (2,0), the factors of f(x) are (x + 6) and (x - 2). The factor in which the coefficient is 1 is therefore (x + 6).