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(A) To divide $p(x) = x^{4} + 0x^{3} + 0x^{2} + 0x + 1$ by $x + 1$,we use the synthetic division method.The zero of the divisor $x + 1$ is $x = -1$.Se

Vedclass · Accepted Answer

Quotient: $x^{3} - x^{2} + x - 1$,Remainder: $2$

Vedclass · Answer

(A) To divide $p(x) = x^{4} + 0x^{3} + 0x^{2} + 0x + 1$ by $x + 1$,we use the synthetic division method.The zero of the divisor $x + 1$ is $x = -1$.Setting up the synthetic division table:$-1$ | $1$  $0$  $0$  $0$  $1$|    $-1$  $1$  $-1$  $1$-----------------------$1$  $-1$  $1$  $-1$  $2$The coefficients of the quotient are $1, -1, 1, -1$,which corresponds to the polynomial $x^{3} - x^{2} + x - 1$.The remainder is the last value,which is $2$.Thus,the quotient is $x^{3} - x^{2} + x - 1$ and the remainder is $2$.

Find the division of the following by synthetic division method: $p(x) = x^{4} + 1$ by $x + 1$.

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