In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):
f(x) = 3x4+2x3, g(x) = x+
We have,
f(x) = 3x4+2x3 and g(x) = x+
Therefore, by remainder theorem when f (x) is divided by g (x) = x – (- ), the remainder is equal to f ()
Now, f(x) = 3x4+2x3
f () = 3 ()4 + 2 ()3 – () - +
= 3 * + 2 * - - +
= - - + +
= =
= 0
Hence, required remainder is 0.