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G10-MATH-C2-L1-QR2

Long and Synthetic Division Involving Polynomials

🍊 Long and Synthetic Division Quiz

Hi, math star! Answer all 30 questions and click DONE when finished. You’ll instantly see your score, the correct answers, and a simple explanation for every item. ✨

This quiz is designed for a Grade 10 level and includes Fundamentals, Solving Multiple Choice, and Matching via Dropdown.

🧠 10 Fundamentals
✍️ 10 Solving MCQ
🔽 10 Dropdown Matching
🎯 Instant Feedback

📘 Part I – Fundamentals

Choose the best answer. These questions test your understanding of the basic ideas behind polynomial long division and synthetic division. 😊

1
Which type of divisor is best suited for synthetic division?
2
In synthetic division, if the divisor is x + 5, the number used in the setup is:
3
Which statement is true about long division of polynomials?
4
Before dividing 4x³ − 7x + 2 by x − 1, what must be inserted in the dividend?
5
What does the Remainder Theorem say?
6
Which divisor cannot be handled directly by basic synthetic division?
7
If the remainder when dividing P(x) by x − 2 is 0, then:
8
In polynomial long division, the first term of the quotient is found by:
9
Which is the correct arrangement of coefficients for 2x⁴ − 3x² + x − 9 in synthetic division?
10
If P(3) = −8, then the remainder when P(x) is divided by x − 3 is:

✍️ Part II – Solving (Multiple Choice)

Now let’s solve! Choose the best answer. These questions involve actual polynomial division and remainders. You’ve got this! 💪

11
Divide 3x³ − 5x² + 2x − 8 by x − 2.
12
What is the remainder when 2x⁴ + 3x³ − 11x² − 12x + 9 is divided by x + 3?
13
Divide x⁴ − 16 by x − 2.
14
If P(x)=2x³ + 7x² − 4x + 5, what is the remainder when P(x) is divided by x + 1?
15
Divide 4x³ − 13x + 6 by x + 2.
16
Find the quotient when 6x⁴ − 7x³ + 5x − 2 is divided by x − 1.
17
Divide x³ − 6x² + 11x − 6 by x − 3.
18
What is the remainder when 5x⁴ − 4x³ + 3x² − 2x + 7 is divided by x + 1?
19
Which binomial is a factor of x³ − 4x² − x + 4?
20
Divide 2x⁴ − x³ + 3x − 10 by x − 2. What is the quotient?

🔽 Part III – Matching Type with Dropdown

For each item, choose the correct answer from the dropdown. Each dropdown contains the same 10 choices. Read carefully! 🌟

Choices for Items 21–30:
  • A. x² + 3x + 5
  • B. 2x² − 5x + 1
  • C. x² − 4
  • D. 3x² + 6x + 7
  • E. 4x + 9
  • F. 2x³ + x² − 3x + 4
  • G. Remainder = −6
  • H. Remainder = 12
  • I. x³ − 2x² + 4x − 8
  • J. 5x² − 10x + 6
21
Divide x³ + x² − x − 10 by x − 2.
22
Divide 2x³ − 3x² − 4x + 1 by x + 1.
23
Divide x³ − 3x² − 4x + 12 by x − 3.
24
Divide 3x³ + 12x² + 19x + 14 by x + 2.
25
Divide 4x² + 5x − 9 by x − 1.
26
Divide 2x⁴ + 5x³ − x² − 2x + 8 by x + 2.
27
Find the remainder when x³ − 4x² + x is divided by x − 2.
28
Find the remainder when x² + 5x + 18 is divided by x + 3.
29
Divide x⁴ − x³ + 2x² − 4x − 8 by x + 1.
30
Divide 5x³ − 20x² + 26x − 12 by x − 2.

🎉 Quiz Results

Your score: 0 / 30

Green means correct, red means incorrect. Every item now shows the correct answer and explanation. Keep practicing — you’re getting stronger in polynomial division! 🍊