Answer:
remainder = 0
Step-by-step explanation:
Using the Remainder Theorem
Given f(x) divided by (x + h) then the remainder is found by evaluating f(- h)
Here the divisor is (x + 2), hence evaluate at h = - 2
Let f(x) = 3[tex]x^{4}[/tex] + 2x³ - x² + 2x - 24, then
f(- 2) = 3[tex](-2)^{4}[/tex] + 2(- 2)³ - (- 2)² + 2(- 2) - 24
= 3(16) + 2(- 8) - 4 - 4 - 24
= 48 - 16 - 4 - 4 - 24 = 0 ← Remainder
Remainder = 0 , hence (x + 2) is a factor of f(x)
