Use factor theorem to find whether polynomial g(x) is a factor of poly

1.	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» 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).

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»

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).