X2-x3+2x2+x+1 by X-1 Synthetic method

April 9, 2026Mathematics

ScanSolve AI Answer

April 9, 2026

Answer

$x^2 + 2x + 3 + \frac{4}{x-1}$

We want to divide the polynomial $x^3 - x^2 + 2x^2 + x + 1$ by $x-1$ . First, simplify the polynomial: $x^3 + x^2 + x + 1$ .

Using synthetic division with the root $1$ from the divisor $x-1$ :

1 | 1   1   1   1
  |     1   2   3
  ----------------
    1   2   3   4

The coefficients of the quotient are $1, 2, 3$ , and the remainder is $4$ .

The quotient is $x^2 + 2x + 3$ and the remainder is $4$ .

So, $\frac{x^3 + x^2 + x + 1}{x-1} = x^2 + 2x + 3 + \frac{4}{x-1}$ .

The final answer is $\boxed{x^2 + 2x + 3 + \frac{4}{x-1}}$ .

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Quick Answer

We want to divide the polynomial x^3 - x^2 + 2x^2 + x + 1 by x-1. First, simplify the polynomial: x^3 + x^2 + x + 1.

Asked on April 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 9, 2026

We want to divide the polynomial x^3 - x^2 + 2x^2 + x + 1 by x-1. First, simplify the polynomial: x^3 + x^2 + x + 1. Using synthetic division with the root 1 from the divisor x-1: ` 1 | 1 1 1 1 | 1 2 3 ---------------- 1 2 3 4 ` The coefficients of the quotient are 1, 2, 3, and the remainder is 4. The quotient is x^2 + 2x + 3 and the remainder is 4. So, (x^3 + x^2 + x + 1)/(x-1) = x^2 + 2x + 3 + (4)/(x-1). The final answer is x^2 + 2x + 3 + (4)/(x-1).