- The problem shows polynomial long division of $x^3 - 3x^2 + 3x - 2$ by $x - 2$.
- Step 1: Divide the leading term of the dividend ($x^3$) by the leading term of the divisor ($x$), giving $x^2$. Write $x^2$ above the division bar.
- Multiply $x^2$ by the divisor $x - 2$, resulting in $x^3 - 2x^2$. Subtract this from the first two terms of the dividend: $(x^3 - 3x^2) - (x^3 - 2x^2) = -x^2$.
- Bring down the next term, $+3x$, to get $-x^2 + 3x$.
- Step 2: Divide $-x^2$ by $x$, giving $-x$. Write $-x$ above the division bar.
- Multiply $-x$ by $x - 2$, resulting in $-x^2 + 2x$. Subtract this from $-x^2 + 3x$: $(-x^2 + 3x) - (-x^2 + 2x) = x$.
- Bring down the next term, $-2$, to get $x - 2$.
- Step 3: Divide $x$ by $x$, giving $+1$. Write $+1$ above the division bar.
- Multiply $+1$ by $x - 2$, resulting in $x - 2$. Subtract this from $x - 2$: $(x - 2) - (x - 2) = 0$.
- The remainder is 0, so the division is exact.
- The quotient is $x^2 - x + 1$.
Parent Tip: Review the logic above to help your child master the concept of dividing polynomials using long division worksheet.
