Grade 10 Exam > Grade 10 Questions > If f(x) is divided by g(x), it gives quotient...
Start Learning for Free
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.
- a)True
- b)False
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as...
Consider, f(x) is 27x2 - 39x, q(x) as 9x + 2, g(x) as 3x - 5 and remainder is 10.
f(x) = q(x) × g(x) + r(x)
RHS
q(x) × g(x) + r(x) = (9x + 2)(3x - 5) + 10 = 27x2 - 45x + 6x - 10 + 10 = 27x2 - 39x, which is equal to LHS.
Hence proved.
f(x) = q(x) × g(x) + r(x)
RHS
q(x) × g(x) + r(x) = (9x + 2)(3x - 5) + 10 = 27x2 - 45x + 6x - 10 + 10 = 27x2 - 39x, which is equal to LHS.
Hence proved.
Most Upvoted Answer
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as...
Understanding Polynomial Division
When dividing one polynomial by another, the relationship between the dividend, divisor, quotient, and remainder is critical to understand.
Key Components of Polynomial Division
- Dividend (f(x)): This is the polynomial that is being divided.
- Divisor (g(x)): This is the polynomial by which the dividend is divided.
- Quotient (q(x)): This is the result of the division, representing how many times the divisor fits into the dividend.
- Remainder (r(x)): This is what is left over after the division process is completed.
The Division Algorithm
The fundamental principle behind polynomial division can be summarized in the equation:
- f(x) = q(x) × g(x) + r(x)
This equation holds true under the following conditions:
- The degree of the remainder (r(x)) must be less than the degree of the divisor (g(x)).
- The quotient (q(x)) and remainder (r(x)) are uniquely determined by the dividend and divisor.
Why is this True?
- Complete Representation: The equation captures all components of the division process, showing how the dividend can be fully expressed in terms of the divisor, quotient, and remainder.
- Mathematical Foundation: This formula is derived from the properties of polynomial division, similar to numerical long division, ensuring that every instance of division adheres to this structure.
In summary, the statement that "f(x) = q(x) × g(x) + r(x)" is indeed true, affirming the core principles of polynomial division.
When dividing one polynomial by another, the relationship between the dividend, divisor, quotient, and remainder is critical to understand.
Key Components of Polynomial Division
- Dividend (f(x)): This is the polynomial that is being divided.
- Divisor (g(x)): This is the polynomial by which the dividend is divided.
- Quotient (q(x)): This is the result of the division, representing how many times the divisor fits into the dividend.
- Remainder (r(x)): This is what is left over after the division process is completed.
The Division Algorithm
The fundamental principle behind polynomial division can be summarized in the equation:
- f(x) = q(x) × g(x) + r(x)
This equation holds true under the following conditions:
- The degree of the remainder (r(x)) must be less than the degree of the divisor (g(x)).
- The quotient (q(x)) and remainder (r(x)) are uniquely determined by the dividend and divisor.
Why is this True?
- Complete Representation: The equation captures all components of the division process, showing how the dividend can be fully expressed in terms of the divisor, quotient, and remainder.
- Mathematical Foundation: This formula is derived from the properties of polynomial division, similar to numerical long division, ensuring that every instance of division adheres to this structure.
In summary, the statement that "f(x) = q(x) × g(x) + r(x)" is indeed true, affirming the core principles of polynomial division.
|
Explore Courses for Grade 10 exam
|
|
Similar Grade 10 Doubts
Top Courses for Grade 10View all
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
Question Description
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? for Grade 10 2025 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Grade 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?.
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? for Grade 10 2025 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Grade 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Grade 10.
Download more important topics, notes, lectures and mock test series for Grade 10 Exam by signing up for free.
Here you can find the meaning of If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then, f(x) = q(x) × g(x) + r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Grade 10 tests.
|
|
Explore Courses for Grade 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup