Answer:Step-by-step explanation:We have given:x^4-2/x+1Put x+1 = 0x= 0-1x= -1-1 | 1 0 0 0 -2 | -1 1 -1 1_______________ 1 -1 1 -1 -1Thus it makes the expression: x^3-x^2+x-1 - 1/x+1You can further confirm this expression by solving the expression: (x4 − 2) ÷ (x + 1).x^4 - 1 -1/x+1x^4-1/x+1 - 1/x+1(x^2-1) (x^2+1)/x+1 - 1/x+1(x-1)(x+1) (x^2+1)/x+1 - 1/x+1x+1 n the numerator will be cancelled out by x+1 in the denominator.(x-1) (x^2+1) - 1/x+1Multiply (x^2+1) by x-1x(x^2+1) -1(x^2+1) - 1/x+1x^3+x-x^2-1 - 1/x+1x^3-x^2+x-1 - 1/x+1 ....