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G10-MATH-C2-L1-QR4

Long and Synthetic Division

💙 Long and Synthetic Division Quiz

Hello, math explorer! Answer all 30 questions, then click DONE to check your work. You’ll see the correct answers, explanations, and solution steps right away. ✨

This quiz has 10 fundamentals, 10 multiple-choice solving items, and 10 dropdown matching items.

📘 Fundamentals
✍️ Solving
🔽 Dropdown Matching
🌟 Instant Feedback

📘 Part I – Fundamentals

Choose the best answer. These questions check your understanding of key ideas in polynomial long division and synthetic division. 😊

1
Which divisor can be used directly in synthetic division?
2
If the divisor is x – 7, what number is placed outside the synthetic division box?
3
When using synthetic division for 5x^4 – 2x + 9, which missing terms must be included?
4
What theorem lets you find the remainder of dividing P(x) by x – a using P(a)?
5
If P(-2)=0, which statement must be true?
6
In polynomial long division, what do you do immediately after finding the next term in the quotient?
7
Which coefficient list correctly represents 3x^5 – x^3 + 4x – 8 for synthetic division?
8
Which expression shows a polynomial division result written correctly?
9
If a polynomial is divided by x – 5, which value should be substituted into P(x) to find the remainder?
10
Why is long division more general than synthetic division?

✍️ Part II – Solving (Multiple Choice)

Solve carefully and choose the best answer. These are different from the previous set and slightly challenging for Grade 10. 💪

11
Divide 2x^3 + x^2 – 7x + 6 by x – 2.
12
What is the remainder when x^4 – 3x^3 + 2x – 9 is divided by x + 1?
13
Divide 3x^3 – 4x^2 + x – 10 by x + 2.
14
Divide x^3 – 5x^2 + 6x – 8 by x – 4. What is the quotient?
15
Find the remainder when 2x^4 – x^2 + 5x + 1 is divided by x – 3.
16
Which binomial is a factor of x^3 + x^2 – 4x – 4?
17
Divide 4x^4 + 0x^3 – 8x^2 + 7x – 3 by x + 1. What is the quotient?
18
Divide 5x^3 – 6x^2 – x + 14 by x – 2. What is the remainder?
19
Divide x^4 + 2x^3 – x + 6 by x – 1.
20
Divide 2x^3 – 9x^2 + 13x – 6 by x – 3. What is the quotient?

🔽 Part III – Matching Type with Dropdown

Each question has the same 10 choices in the dropdown. Choose the correct one for each item. 🌈

Choices for Items 21–30:
  • A. x^2 + x – 5
  • B. 2x^2 + 3x + 1
  • C. x^2 – 2x – 3
  • D. 3x^2 – 4x + 2
  • E. 4x – 7
  • F. 2x^3 – x^2 + 4x – 9
  • G. Remainder = 5
  • H. Remainder = -10
  • I. x^3 + 2x^2 – 3x + 6
  • J. 5x^2 + x – 4
21
Divide x^3 – 4x – 10 by x – 2.
22
Divide 2x^3 + 7x^2 + 7x + 1 by x + 2.
23
Divide x^3 – 5x^2 + x + 3 by x – 3.
24
Divide 3x^3 – x^2 – 10x + 8 by x – 1.
25
Divide 4x^2 + x – 11 by x + 2.
26
Divide 2x^4 + 3x^3 + 2x^2 + 6x – 9 by x + 2.
27
Find the remainder when x^2 – 3x + 7 is divided by x – 1.
28
Find the remainder when x^3 – 2x^2 + 4x – 20 is divided by x – 2.
29
Divide x^4 + 3x^3 + x + 6 by x + 1.
30
Divide 5x^3 + 6x^2 – 3x – 4 by x + 1.

🎉 Quiz Results

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