Divide x4 -2 by x+1

Question

Lesson 21 problem number 25

Answer 1

Well!

 

I think you meant (x^4 - 2) / (x+1)

 

(x^4 - 2) / (x+1)

Writing it in polynomial form with co-efficients

x^4 - 2 = 1 x^4 + 0 x^3 + 0 x^2 + 0 x - 2

 

Now, writing the co-efficients alone, for synthetic division

Synthetic Division

x	c		x^4	x^3	x^2	x	c		Value	Poly
1	1		1	0	0	0	-2
			1	1					1	x^3
			0	-1	0	0	-2			REM
				-1	-1				-1	x^2
				0	+1	0	-2			REM
					1	1			1	x
					0	-1	-2			REM
						-1	-1		-1	c
						0	-1			REM

Further Division is not Possible.

Thus, (x^4 - 2) / (x+1)

Quotient: x^3 - x^2 + x -1

Remainder: -1