Algebra 2 Polynomial Long Division Exam Prep Questions

📚 Quick Study Guide

• 🔢 Polynomial long division is used to divide a polynomial by another polynomial of a lower or equal degree.
• ✍️ The process is similar to long division with numbers. We divide, multiply, subtract, and bring down the next term.
• ➗ The division process continues until the degree of the remainder is less than the degree of the divisor.
• 💡 Remember the division algorithm: Dividend = (Divisor × Quotient) + Remainder
• 📝 When writing your answer, include any remainder as a fraction over the divisor.
• 🧮 Make sure the polynomial is written in descending order of exponents and include placeholders (0x^n) for missing terms.
• ➕ Be careful with signs during the subtraction step.

Practice Quiz

1. What is the quotient when $x^3 - 8$ is divided by $x - 2$?
1. $x^2 - 2x + 4$
2. $x^2 + 2x + 4$
3. $x^2 - 4$
4. $x^2 + 4$
2. Divide $(2x^3 + 5x^2 - 7x - 10)$ by $(x + 3)$. What is the remainder?
1. 5
2. -1
3. 2
4. -4
3. Perform the division: $\frac{x^4 - 1}{x - 1}$
1. $x^3 + x^2 + x + 1$
2. $x^3 - x^2 + x - 1$
3. $x^3 + 1$
4. $x^3 - 1$
4. What is the result of $(3x^3 - 2x + 1)$ divided by $(x + 1)$?
1. $3x^2 - 3x + 1 + \frac{2}{x+1}$
2. $3x^2 + 3x - 5 + \frac{6}{x+1}$
3. $3x^2 - 3x + 1 - \frac{2}{x+1}$
4. $3x^2 - 3x + 5 - \frac{4}{x+1}$
5. If $(x^3 + 4x^2 + x - 6)$ is divided by $(x + 2)$, what is the quotient?
1. $x^2 + 2x - 3$
2. $x^2 + 6x + 13$
3. $x^2 - 2x + 3$
4. $x^2 - 6x - 11$
6. What is the quotient and remainder when $(2x^4 - x^3 + 5x - 3)$ is divided by $(x^2 + 1)$?
1. Quotient: $2x^2 - x - 2$, Remainder: $6x - 1$
2. Quotient: $2x^2 - x + 2$, Remainder: $3x - 5$
3. Quotient: $2x^2 + x - 2$, Remainder: $x + 1$
4. Quotient: $2x^2 + x + 2$, Remainder: $-3x - 1$
7. Find the remainder when $x^{100} - 1$ is divided by $x - 1$.
1. 0
2. 1
3. 2
4. -1