Subtract 2x2+x+1 from 4x2+3x+5. What is the result? a. 2x2+2x+4 b. 2x2+4x+4 c. 2x2+2x+3 d. 4x2+2x+5 Add the polynomials 3x2+4x+5 and 2x2+x+3. What is the result? a. 5x2+5x+8 b. 5x2+5x+15 c. 4x2+5x+8 d. 5x2+5x+7 What is the sum of 4x2+2x+3 and x2+3x+5? a. 5x2+5x+8 b. 4x2+5x+8 c. 5x2+x+8 d. 5x2+6x+8 Subtract 2x2+3x+4 from 5x2+6x+7. What is the result? a. 4x2+3x+3 b. 3x2+4x+3 c. 3x2+3x+2 d. 3x2+3x+3 Add the polynomials x2+4x+4 and 2x2+3x+1. What is the result? a. 3x2+6x+5 b. 3x2+6x+4 c. 3x2+7x+5 d. 3x2+7x+1 What is the result of adding 3x2+2x+1 and 2x2+4x+3? a. 5x2+6x+1 b. 5x2+6x+4 c. 5x2+6x+2 d. 5x2+7x+4 What is the product of (2x+5) and (x−3)? a. 2x2−x−15 b. 2x2+x−15 c. 2x2−5x−15 d. 2x2−5x+15 Add the polynomials 2x2+6x+4 and 3x2+4x+5. What is the result? a. 4x2+7x+9 b. 5x2+7x+8 c. 5x2+10x+9 d. 5x2+6x+9 What is the product of (x−4) and (x+3)? a. x2−2x−12 b. x2+x−12 c. x2−x−12 d. x2−x+12 Subtract 2x2+4x+6 from 6x2+5x+7. What is the result? a. 4x2+x+2 b. 3x2+x+1 c. 4x2+x+1 d.

### Solutions:

---

**1. Subtract \( 2x^2 + x + 1 \) from \( 4x^2 + 3x + 5 \):**  
\[
(4x^2 + 3x + 5) - (2x^2 + x + 1) = 4x^2 - 2x^2 + 3x - x + 5 - 1 = 2x^2 + 2x + 4.
\]  
**Answer:** \( \mathbf{a. \ 2x^2 + 2x + 4} \).

---

**2. Add \( 3x^2 + 4x + 5 \) and \( 2x^2 + x + 3 \):**  
\[
(3x^2 + 4x + 5) + (2x^2 + x + 3) = 3x^2 + 2x^2 + 4x + x + 5 + 3 = 5x^2 + 5x + 8.
\]  
**Answer:** \( \mathbf{a. \ 5x^2 + 5x + 8} \).

---

**3. Add \( 4x^2 + 2x + 3 \) and \( x^2 + 3x + 5 \):**  
\[
(4x^2 + 2x + 3) + (x^2 + 3x + 5) = 4x^2 + x^2 + 2x + 3x + 3 + 5 = 5x^2 + 5x + 8.
\]  
**Answer:** \( \mathbf{a. \ 5x^2 + 5x + 8} \).

---

**4. Subtract \( 2x^2 + 3x + 4 \) from \( 5x^2 + 6x + 7 \):**  
\[
(5x^2 + 6x + 7) - (2x^2 + 3x + 4) = 5x^2 - 2x^2 + 6x - 3x + 7 - 4 = 3x^2 + 3x + 3.
\]  
**Answer:** \( \mathbf{d. \ 3x^2 + 3x + 3} \).

---

**5. Add \( x^2 + 4x + 4 \) and \( 2x^2 + 3x + 1 \):**  
\[
(x^2 + 4x + 4) + (2x^2 + 3x + 1) = x^2 + 2x^2 + 4x + 3x + 4 + 1 = 3x^2 + 7x + 5.
\]  
**Answer:** \( \mathbf{c. \ 3x^2 + 7x + 5} \).

---

**6. Add \( 3x^2 + 2x + 1 \) and \( 2x^2 + 4x + 3 \):**  
\[
(3x^2 + 2x + 1) + (2x^2 + 4x + 3) = 3x^2 + 2x^2 + 2x + 4x + 1 + 3 = 5x^2 + 6x + 4.
\]  
**Answer:** \( \mathbf{b. \ 5x^2 + 6x + 4} \).

---

**7. Product of \( (2x + 5) \) and \( (x - 3) \):**  
Using distributive property:
\[
(2x + 5)(x - 3) = 2x \cdot x + 2x \cdot (-3) + 5 \cdot x + 5 \cdot (-3) = 2x^2 - 6x + 5x - 15 = 2x^2 - x - 15.
\]  
**Answer:** \( \mathbf{a. \ 2x^2 - x - 15} \).

---

**8. Add \( 2x^2 + 6x + 4 \) and \( 3x^2 + 4x + 5 \):**  
\[
(2x^2 + 6x + 4) + (3x^2 + 4x + 5) = 2x^2 + 3x^2 + 6x + 4x + 4 + 5 = 5x^2 + 10x + 9.
\]  
**Answer:** \( \mathbf{c. \ 5x^2 + 10x + 9} \).

---

**9. Product of \( (x - 4) \) and \( (x + 3) \):**  
Using distributive property:
\[
(x - 4)(x + 3) = x \cdot x + x \cdot 3 + (-4) \cdot x + (-4) \cdot 3 = x^2 + 3x - 4x - 12 = x^2 - x - 12.
\]  
**Answer:** \( \mathbf{a. \ x^2 - x - 12} \).

---

**10. Subtract \( 2x^2 + 4x + 6 \) from \( 6x^2 + 5x + 7 \):**  
\[
(6x^2 + 5x + 7) - (2x^2 + 4x + 6) = 6x^2 - 2x^2 + 5x - 4x + 7 - 6 = 4x^2 + x + 1.
\]  
**Answer:** \( \mathbf{c. \ 4x^2 + x + 1} \).

---

### Follow-up Questions:
1. Can you explain why combining like terms is essential in polynomial operations?
2. How does the distributive property simplify the multiplication of binomials?
3. What strategies can help avoid errors when subtracting polynomials?
4. How can you check your work after performing polynomial addition or subtraction?
5. What are the common mistakes students make when working with polynomials, and how can they be avoided?

### Tip:
Always write each step clearly when working with polynomials to avoid missing terms or signs!

Subtract 2x2+x+1 from 4x2+3x+5. What is the result? a. 2x2+2x+4 b. 2x2+4x+4 c. 2x2+2x+3 d. 4x2+2x+5 Add the polynomials 3x2+4x+5 and 2x2+x+3. What is the result? a. 5x2+5x+8 b. 5x2+5x+15 c. 4x2+5x+8 d. 5x2+5x+7 What is the sum of 4x2+2x+3 and x2+3x+5? a. 5x2+5x+8 b. 4x2+5x+8 c. 5x2+x+8 d. 5x2+6x+8 Subtract 2x2+3x+4 from 5x2+6x+7. What is the result? a. 4x2+3x+3 b. 3x2+4x+3 c. 3x2+3x+2 d. 3x2+3x+3 Add the polynomials x2+4x+4 and 2x2+3x+1. What is the result? a. 3x2+6x+5 b. 3x2+6x+4 c. 3x2+7x+5 d. 3x2+7x+1 What is the result of adding 3x2+2x+1 and 2x2+4x+3? a. 5x2+6x+1 b. 5x2+6x+4 c. 5x2+6x+2 d. 5x2+7x+4 What is the product of (2x+5) and (x−3)? a. 2x2−x−15 b. 2x2+x−15 c. 2x2−5x−15 d. 2x2−5x+15 Add the polynomials 2x2+6x+4 and 3x2+4x+5. What is the result? a. 4x2+7x+9 b. 5x2+7x+8 c. 5x2+10x+9 d. 5x2+6x+9 What is the product of (x−4) and (x+3)? a. x2−2x−12 b. x2+x−12 c. x2−x−12 d. x2−x+12 Subtract 2x2+4x+6 from 6x2+5x+7. What is the result? a. 4x2+x+2 b. 3x2+x+1 c. 4x2+x+1

Learn how to solve polynomial operations, including addition, subtraction, and multiplication. This problem set covers key algebraic concepts, such as combining like terms, the distributive property, and simplification. Suitable for Grades 7-9, complete with step-by-step solutions and explanations.

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