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)
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