- The solution for problem 17 is incorrect. The dividend is $x^4 + 5x^3 + 6x^2$, which means the coefficients are 1, 5, 6, 0, 0 (for $x^4, x^3, x^2, x^1, x^0$). The synthetic division was performed correctly with these coefficients and the root -3, yielding a quotient of $x^3 + 2x^2 + 0x + 0$, or simply $x^3 + 2x^2$. The final answer should be $x^3 + 2x^2$, not $x^3 + 2x$.
- The solution for problem 18 is correct. The polynomial division $(t^5 - 6t^3 - 7t^2 - t - 15) \div (t - 3)$ was performed using synthetic division with the root 3. The resulting quotient is $t^4 + 3t^3 + 3t^2 + 2t + 5$, which matches the provided answer.
- The solution for problem 19 is correct. The division $\frac{h^2 + 2h + 2}{h + 3}$ was performed using synthetic division with the root -3. The result is a quotient of $h - 1$ and a remainder of 5, expressed as $h - 1 + \frac{5}{h+3}$.
- The solution for problem 20 is correct. The division $(8x^2 + 14x + 5) \div (2x + 1)$ was performed using long division. The quotient is $4x + 5$, and the remainder is 0, which is correct. The work shown on the right side also verifies this result by factoring the numerator as $(2x + 1)(4x + 5)$, confirming the division.
Parent Tip: Review the logic above to help your child master the concept of synthetic division worksheet with answers.
