use synthetic division to solve $(x^{4}-1)div(x - 1)$. what is the quotient?\n$x^{3}-x^{2}+x…

Answer:

C. $x^{3}+x^{2}+x + 1$

Explanation:

Step1: Set up synthetic division

The divisor is $x - 1$, so the zero is $c=1$. The dividend is $x^{4}+0x^{3}+0x^{2}+0x - 1$, so the coefficients are $1,0,0,0,-1$.

Step2: Bring down the first coefficient

Bring down the first coefficient $1$.

Step3: Multiply and add

Multiply $1$ (the zero) by $1$ (the brought - down coefficient) to get $1$, and add to the next coefficient $0$: $0 + 1=1$.

Step4: Repeat multiplication and addition

Multiply $1$ by $1$ to get $1$, add to the next coefficient $0$: $0+1 = 1$. Multiply $1$ by $1$ to get $1$, add to the next coefficient $0$: $0 + 1=1$. Multiply $1$ by $1$ to get $1$, add to the last coefficient $-1$: $-1+1 = 0$. The coefficients of the quotient are $1,1,1,1$, so the quotient is $x^{3}+x^{2}+x + 1$.