Question

division to divide $x^3 - x^2 + 2x - 1$ by $x - 2$
the quotient is:
the remainder is:
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Explanation:

Step1: Identify root of divisor

For divisor $x-2$, root is $2$.

Step2: Set up synthetic division

Top row: $1, -1, 2, -1$; Left box: $2$

Step3: Bring down leading coefficient

First bottom box: $1$

Step4: Multiply, add to next coefficient

$1 \times 2 = 2$; $-1 + 2 = 1$
Middle top box 1: $2$; Bottom box 2: $1$

Step5: Multiply, add to next coefficient

$1 \times 2 = 2$; $2 + 2 = 4$
Middle top box 2: $2$; Bottom box 3: $4$

Step6: Multiply, add to last coefficient

$4 \times 2 = 8$; $-1 + 8 = 7$
Middle top box 3: $8$; Bottom box 4: $7$

Step7: Find quotient and remainder

Quotient: $x^2 + x + 4$; Remainder: $7$

Answer:

Left top box: $2$
Middle top boxes (left to right): $2$, $2$, $8$
Bottom boxes (left to right): $1$, $1$, $4$, $7$
The quotient is: $x^2 + x + 4$
The remainder is: $7$