Which statements are true about the polynomial function?

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)

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