Is the binomial a factor of the polynomial function? f(x)=x^3+3x^2−25x−75 select yes or no for each binomial. yes no (choose yes or no for each binomial) (x−1) (x−3) (x+3) (x−5) (x+5)

To check if the binomial is a factor, we take it in the form of x – c = 0 and then x = c, then substitute the value of c into x on the polynomial equation. It is only a factor when the value of f(x) = 0

a. x – 1

x = 1

Substitute x = 1 into the equation.

f(x) = 1^3 + 3 * 1^2 – 25 * 1 – 75

f(x) = -96

(not a factor)

b. x – 3

x = 3

Substitute x = 3 into the equation.

f(x) = 3^3 + 3 * 3^2 – 25 * 3 – 75

f(x) = -96

(not a factor)

c. x + 3

x = -3

Substitute x = 3 into the equation.

f(x) = (-3)^3 + 3 * (-3)^2 – 25 * (-3) – 75

f(x) = 0

(a factor)

d. x - 5

x = 5

Substitute x = 3 into the equation.

f(x) = 5^3 + 3 * 5^2 – 25 * 5 – 75

f(x) = 0

(a factor)

e. x + 5

x = - 5

Substitute x = 3 into the equation.

f(x) = (-5)^3 + 3 * (-5)^2 – 25 * (-5) – 75

f(x) = 0

(a factor)

1.No

2.No

3.yes

4.No

5.No

step-by-step explanation:

the true ones are a b and d

step-by-step explanation: