Question

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

 x⁴ − x³ + 5x, x − 1

Answer 1

\[\frac{x^4 {-x}^3 +5x}{x-1}\]
\[ = \frac{x^3 (x-1)+5(x-1)+5}{x-1}\]
\[ = \frac{{(x-1)(x}^3 +5)+5}{x-1}\]
\[ {=(x}^3 +5)+ \frac{5}{x - 1}\]
\[\text{Therefore, quotient} = x^3 +5\ \text{and remainder = 5 .}\]