Question

Divide x³ + 1 by x + 1 and find quotient and remainder.​

Answer 1

Given :-

It is given to divide x³ + 1 by x + 1 and find quotient and remainder.

Solution :-

We can divide x³ + 1 by x + 1 by the method below;

x³ + 1 = (x + 1)(x² - x + 1)

⇒ x³ + 1/(x + 1) = (x + 1)(x² - x + 1)/x + 1

⇒ (x² - x + 1)

∴ Hence, after the division, the quotient against the division will be (x² - x + 1) and the remainder will be 0 as x³ + 1 is perfectly divisible by x + 1.