find remainder for x5 - 3x3 + x2 - 3 by x-1

Question

 Find the remainder when x⁵ - 3x³ + x² - 3 is divided by: 
                a)  x - 1  

Answer 1

  

The Remainder Theorem:

When you divide a polynomial f(x) by x - a the remainder r will be f(a).

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

According to the Remainder Theorem:f(1) is the remaider.

f(1) = 1⁵ - 3(1)³ + (1)² - 3

        =1-3+1-3

        =-4

-4 is the Remainder