- Divide the leading term of the dividend, $x^3$, by the leading term of the divisor, $2x$, to get $\frac{1}{2}x^2$. This is the first term of the quotient.
- Multiply the entire divisor $(2x - 4)$ by $\frac{1}{2}x^2$ to get $x^3 - 2x^2$.
- Subtract this result from the original dividend: $(x^3 - 2x^2 + 3x + 6) - (x^3 - 2x^2) = 3x + 6$.
- Divide the leading term of the new polynomial, $3x$, by the leading term of the divisor, $2x$, to get $\frac{3}{2}$.
- Multiply the entire divisor $(2x - 4)$ by $\frac{3}{2}$ to get $3x - 6$.
- Subtract this result from the current polynomial: $(3x + 6) - (3x - 6) = 12$.
- The remainder is 12, and since its degree is less than the degree of the divisor, the division process stops.
- The final answer is the quotient plus the remainder over the divisor: $\frac{1}{2}x^2 + \frac{3}{2} + \frac{12}{2x - 4}$.
Parent Tip: Review the logic above to help your child master the concept of wizzred long division.
