Use synthetic division to perform the division.
$\frac{x^{4} + x^{3} + 4 x^{2} + 5 x + 1}{x + 1}$

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Answer

$x^{3} + 3 x + 2 - \frac{1}{x + 1}$ is the final result of the synthetic division.

Steps

Step 1 ：The given problem is to perform synthetic division on the polynomial $x^{4} + x^{3} + 4 x^{2} + 5 x + 1$ by the divisor $x + 1$ .

Step 2 ：Synthetic division is a shorthand method of dividing polynomials where we divide the coefficients of the polynomial with the divisor.

Step 3 ：Performing the synthetic division, we get the quotient as $x^{3} + 0 x^{2} + 3 x + 2$ and the remainder as $- 1$ .

Step 4 ： $x^{3} + 3 x + 2 - \frac{1}{x + 1}$ is the final result of the synthetic division.