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G10-MATH-C2-L1-QR5

Long and Synthetic Division Involving Polynomials

💙 Long and Synthetic Division Involving Polynomials

Hello, math learner! This interactive quiz is based on the lesson in your book about long division and synthetic division involving polynomials. Answer all 30 questions, then click DONE to see your score, the correct answers, and the solution steps. ✨

📘 10 Fundamentals ✍️ 10 Solving MCQ 🔽 10 Dropdown Matching ✅ Instant Feedback

📘 Part I – Fundamentals

Choose the best answer. These questions follow the ideas shown in the book pages: arranging in descending order, using 0 for missing terms, long division steps, and synthetic division setup. 😊

1
In polynomial long division, the dividend and divisor should be arranged in:
2
If a term is missing in a polynomial, what should be used as its placeholder coefficient?
3
Synthetic division is used when the divisor is a binomial of the form:
4
If the divisor is x + 3, what value is used in synthetic division?
5
In synthetic division, the very first step is to:
6
The last number in the bottom row of a synthetic division table represents the:
7
If a third-degree polynomial is divided by a first-degree polynomial, the quotient is usually of degree:
8
Which expression is the correct general form of a division result?
9
Which coefficient list is correct for 4x3 − 3x + 5 in synthetic division?
10
In long division, after dividing the leading terms, the next step is to:

✍️ Part II – Solving (Multiple Choice)

Choose the best answer. These are new problems from the same topic and are a bit more challenging, just right for Grade 10. 💪

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

🔽 Part III – Solving with One Set of Choices

For items 21–30, choose the correct answer from the dropdown. Every dropdown has the same 10 choices. Read carefully — some ask for a quotient, and some ask for a remainder. 🌟

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

🎉 Quiz Results

Your score: 0 / 30

Green means correct, red means incorrect. Every question shows the correct answer and an explanation after you click DONE. Keep practicing — you’re doing great! 💙