f(x) = 0 when x = - 5
f(x) divided by (x + 5) has a remainder of 0
Using the remainder/ factor theorem
If x = a is a root of a polynomial f(x), then
f(a) = 0 and (x - a) is a factor
f(5) =
+5(5)³ - (5)² - 5(5)
= 625 + 625 - 25 - 25 ≠ 0 ⇒ (x - 5) is not a factor
f(-5) =
+ 5(- 5)³ - (- 5)² - 5(- 5)
= 625 - 625 - 25 + 25 = 0
since f(- 5) = 0 then (x + 5) is a factor of f(x)