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Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1?
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Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - ...
Check for Multiplicity of Polynomials
Given Polynomials:
- p(x) = 2x³ - 11x² - 4x + 5
- g(x) = 2x - 1
Evaluating p(x)/g(x):
- Perform polynomial division to check if p(x) is a multiple of g(x).
- Divide p(x) by g(x) to see if the remainder is zero.
Polynomial Division:
- Divide p(x) = 2x³ - 11x² - 4x + 5 by g(x) = 2x - 1.
- Perform long division or synthetic division to simplify the process.
Result of Division:
- If the remainder is zero, then p(x) is a multiple of g(x).
- If the remainder is not zero, then p(x) is not a multiple of g(x).
Conclusion:
- By evaluating the division, determine whether p(x) is a multiple of g(x) or not.
- Use the remainder to make the final conclusion.
Given Polynomials:
- p(x) = 2x³ - 11x² - 4x + 5
- g(x) = 2x - 1
Evaluating p(x)/g(x):
- Perform polynomial division to check if p(x) is a multiple of g(x).
- Divide p(x) by g(x) to see if the remainder is zero.
Polynomial Division:
- Divide p(x) = 2x³ - 11x² - 4x + 5 by g(x) = 2x - 1.
- Perform long division or synthetic division to simplify the process.
Result of Division:
- If the remainder is zero, then p(x) is a multiple of g(x).
- If the remainder is not zero, then p(x) is not a multiple of g(x).
Conclusion:
- By evaluating the division, determine whether p(x) is a multiple of g(x) or not.
- Use the remainder to make the final conclusion.
Community Answer
Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - ...
Solution:
Given, p(x) = 2x³ - 11x² - 4x + 5
Also, g(x) = 2x + 1
We have to check whether p(x) is a multiple of g(x) or not.
We know that if p(x) is a multiple of g(x) then g(x) must be divisible by p(x)
Let g(x) = 0
2x + 1 = 0
2x = -1
x = -1/2
Put x = -1/2 in p(x)
p(2) = 2(-1/2)³ - 11(-1/2)² - 4(-1/2) + 5
= -2/8 - 11/4 + 2 + 5
= -1/4 - 11/4 + 7
= (-1 - 11 + 7(4))/4
= (-1 - 11 + 28)/4
= 16/4
= 4
p(x) ≠ 0
Since the remainder is not zero, g(x) is not divisible by p(x)
Therefore, p(x) is not a multiple of g(x).
Given, p(x) = 2x³ - 11x² - 4x + 5
Also, g(x) = 2x + 1
We have to check whether p(x) is a multiple of g(x) or not.
We know that if p(x) is a multiple of g(x) then g(x) must be divisible by p(x)
Let g(x) = 0
2x + 1 = 0
2x = -1
x = -1/2
Put x = -1/2 in p(x)
p(2) = 2(-1/2)³ - 11(-1/2)² - 4(-1/2) + 5
= -2/8 - 11/4 + 2 + 5
= -1/4 - 11/4 + 7
= (-1 - 11 + 7(4))/4
= (-1 - 11 + 28)/4
= 16/4
= 4
p(x) ≠ 0
Since the remainder is not zero, g(x) is not divisible by p(x)
Therefore, p(x) is not a multiple of g(x).
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Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1?
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Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1?.
Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Check whether p(x) is a multiple of g(x) or not : p(x) = 2x³ - 11x² - 4x 5, g(x) = 2x 1?.
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