Is the binomial a factor of the polynomial function? f (x) = x^3+5x^2-9x-45

Select yes or no for each binomial:

(X-5)

(X+3)

(X-15)

No, Yes, No

Step-by-step explanation:

to determine if the given binomials are factors of f (x)

if (x - a) is a factor of a polynomial then f (a) = 0

f (5) = 5³ + 5 (5) ² - 9 (5) - 45 = 125 + 125 - 45 - 45 = 160 ≠ 0

⇒ (x - 5) is not a factor

f ( - 3) = ( - 3) ³ + 5 ( - 3) ² - 9 ( - 3) - 45 = - 27 + 45 + 27 - 45 = 0

⇒ (x + 3) is a factor

f (15) = 15³ + 5 (15) ² - 9 (15) - 45 ≠ 0

⇒ (x - 15) is not a factor