f(x) = x^3 – 6x^2 – 19x + 84, g(x) = x – 7

Question

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:

f(x) = x³ – 6x² – 19x + 84, g(x) = x – 7

Answer 1

If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0. 

g(x) = x – 7 = 0, then x = 7

Remainder = f(7)

Now, 

f(7) = (7)³ – 6(7)² – 19 x 7 + 84 

= 343 – 294 – 133 + 84 

= 343 + 84 – 294 – 133 

= 0 

Therefore, g(x) is a factor of f(x).