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 + 11x – 6; g(x) = x – 3
Answer» If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0. g(x) = x - 3 = 0 or x = 3 Remainder = f(3) Now, f(3) = (3)³ – 6(3)² + 11 x 3 – 6 = 27 – 54 + 33 – 6 = 60 – 60 = 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 + 11x – 6; g(x) = x – 3

Answer»

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

g(x) = x - 3 = 0

or x = 3

Remainder = f(3)

Now,

f(3) = (3)³ – 6(3)² + 11 x 3 – 6

= 27 – 54 + 33 – 6

= 60 – 60

= 0

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