grade 9 math polynomial operations quiz

📚 Quick Study Guide

• 🔢 Polynomial: An expression with one or more terms, each being a constant multiplied by a variable raised to a non-negative integer power. Example: $3x^2 + 2x - 5$
• ➕ Adding Polynomials: Combine like terms (terms with the same variable and exponent).
• ➖ Subtracting Polynomials: Distribute the negative sign to each term in the second polynomial and then combine like terms.
• умножение Multiplying Polynomials: Use the distributive property (or FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
• ➗ Dividing Polynomials: Use long division or synthetic division.
• 💡 Key Tip: Always simplify your answer by combining like terms.
• 📝 Remember: Pay close attention to the signs when adding, subtracting, multiplying, and dividing.

✏️ Practice Quiz

1. What is the sum of $(2x^2 + 3x - 1)$ and $(x^2 - 5x + 4)$?
   1. $3x^2 - 2x + 3$
   2. $3x^2 + 8x + 3$
   3. $x^2 - 8x + 5$
   4. $2x^4 - 15x^2 - 4$
2. What is the result of subtracting $(x - 4)$ from $(3x + 2)$?
   1. $2x + 6$
   2. $4x - 2$
   3. $-2x - 6$
   4. $2x - 2$
3. What is the product of $(x + 3)$ and $(x - 2)$?
   1. $x^2 + x - 6$
   2. $x^2 - x + 6$
   3. $x^2 + 5x + 6$
   4. $x^2 - 5x - 6$
4. Simplify: $(4x^3 - 2x^2 + x) - (x^3 + 5x^2 - 3x)$
   1. $3x^3 - 7x^2 + 4x$
   2. $5x^3 + 3x^2 - 2x$
   3. $3x^3 + 3x^2 - 2x$
   4. $4x^3 - 6x^2 + 4x$
5. What is $(2x - 1)(3x + 2)$?
   1. $6x^2 + x - 2$
   2. $6x^2 + 7x - 2$
   3. $6x^2 + x + 2$
   4. $5x^2 - x - 2$
6. Divide $(x^2 + 5x + 6)$ by $(x + 2)$. What is the quotient?
   1. $x + 3$
   2. $x + 2$
   3. $x + 6$
   4. $x - 3$
7. Expand: $(x + 4)^2$
   1. $x^2 + 8x + 16$
   2. $x^2 + 16$
   3. $x^2 + 4x + 16$
   4. $x^2 + 8$