Question

Use the factor theorem to determine whether g(x) is a factor of f(x) in f(x) = 5x³ + x² – 5x – 1; g(x) = x + 1

[Factor theorem : If f(x) is a polynomial; f(a) = 0 then (x – a) is a factor of f(x); a ∈ R]

Answer 1

g(x) = x+ 1 = x- a say 

∴ a = – 1 

f(a) = f(- 1) = 5 (- 1)³ + (- 1)² – 5 (- 1) – 1 

= -5 + 1 + 5 – 1 = 0 

∴ x + 1 is a factor of f(x).