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)