Question

Find the remainder when f(x) =
${x}^{5} - {x}^{3} + {3x}^{2} + 3x + 1$
is divided by
${x}^{2} - 1$
​

Answer 1

$\sf \Large Solution!!$

Let's know what the remainder theorem is.

Remainder Theorem → If f(x), a polynomial in x, is divided by (x - a), the remainder = f(a) e.g. If f(x) is divided by (x - 3), the remainder is f(3).

x² - 1 = 0

x² = 1

x = 1 (√1 is 1)

f(x) = x⁵ - x³ + 3x² + 3x + 1

→ Put the value of x.

f(1) = (1)⁵ - (1)³ + 3(1)² + 3(1) + 1

= 1 - 1 + 3 + 3 + 1

= 7

The remainder when f(x) = x⁵ - x³ + 3x² + 3x + 1 is divided by x² - 1 is 7.