Using synthetic division, find (x4 − 2) ÷ (x + 1).

Step-by-step explanation:

We have given:

x^4-2/x+1

Put x+1 = 0

x= 0-1

x= -1

-1 | 1   0   0   0   -2

  |      -1   1   -1     1

    1    -1   1  -1    -1

Thus it makes the expression:

x^3-x^2+x-1 - 1/x+1

You can further confirm this expression by solving the expression:

(x4 − 2) ÷ (x + 1).

x^4 - 1 -1/x+1

x^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+1

x+1 n the numerator will be cancelled out by x+1 in the denominator.

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

Multiply (x^2+1) by x-1

x(x^2+1) -1(x^2+1)  - 1/x+1

x^3+x-x^2-1 - 1/x+1

x^3-x^2+x-1 - 1/x+1

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step-by-step explanation:

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