Question

Determine is (x-3) is a factor of
x^3 - 5x^2 - 4x + 6 using the remainder
theorem:

Answer 1

(x - 3) is not a factor

Explanation:

If (x - h) is a factor of f(x) then f(h) = 0

here

f(x) = x³ - 5x² - 4x + 6 , then

f(3) = 3³ - 5(3)² - 4(3) + 6 = 27 - 5(9) - 12 + 6 = 27 - 45 - 6 = - 24

since f(x) ≠ 0 then (x - 3) is not a factor of f(x)