Question

find the remainder when 2x² - x +1 is divided by 2x + 1 (step wise)

Answer 1

Dividing 2x² - x +1 is divided by 2x + 1
     
                        2x+1)2x²-x+1(x-1 == Quotient
                                 2x²+x 
                               (-)    (-)
                               _______
                                0 -2x+1
                                   -2x -1
                                  (+)  (+)
                                ______
                                         02   = Remainder
                              
Description:
1. Firstly, I multiplied the divisor 2x+1 with x inorder to eliminate x² term
2. Secondly, I multiplied divisor with -1 inorder to eliminate x term

Finally remainder is 2

Answer 2

As we are dividing 2x²-x+1 by 2x+1
Using remainder theorem,
2x+1 =0
⇒x = -1/2
putting this value in the equation,
2x²-x+1
=2×(-1/2)² -(-1/2) +1
=2/4 +1/2 +1 = 2
So the remainder is 2