Question

13. Apply division algorithm to find the quotient and remainder on dividing x4 + 4 by x2 + x + 1​

Answer 1

Answer:

Dividend = 3 x^3+ 4 x^2+ 6x + 93x

3

+4x

2

+6x+9

Divisor = 3x^3+2x+33x

3

+2x+3

Dividend = (Divisor\times quotient)+RemainderDividend=(Divisor×quotient)+Remainder

3 x^3+ 4 x^2+ 6x + 9 = (3x^3+2x+3 \times 3)+4x^23x

3

+4x

2

+6x+9=(3x

3

+2x+3×3)+4x

2

So, quotient = 3

Remainder = 4x^24x

2

To Verify :

3 x^3+ 4 x^2+ 6x + 9 = (9x^3+6x+9)+4x^23x

3

+4x

2

+6x+9=(9x

3

+6x+9)+4x

2

3 x^3+ 4 x^2+ 6x + 9 = 9x^3+6x+4x^2+93x

3

+4x

2

+6x+9=9x

3

+6x+4x

2

+9

So, LHS = RHS