Question

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x):

f(x) = x³ - 6x² + 2x - 4, g(x) = 1 - 2x

Answer 1

We have,

f(x) = x³ - 6x² + 2x - 4 and g(x) = 1 - 2x

Therefore, by remainder theorem when f (x) is divided by g (x) = -2 (x - \(\frac{1}{2})\), the remainder is equal to f \((\frac{1}{2})\)

Now, f(x) = x³ - 6x² + 2x - 4

f\((\frac{1}{2})=(\frac{1}{2})^{3}-6(\frac{1}{2})^{2}+2(\frac{1}{2})-4\)

\(=\frac{1}{8}-\frac{3}{2}+1-4\)

\(=\frac{-35}{8}\)

Hence, required remainder is \(\frac{-35}{8}\)