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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.
Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of assertion (A) i...
p(x) = x4 + x3 + 2x2 + 4x - 8
p(-2) = (-2)4 + (-2)3 + 2(-2)2 + 4 (-2) - 8
= 16 - 8 + 8 - 8 - 8 = 0
So, (x + 2) is a factor of p(x).
p(1) = (1)4 + (1)3 + 2(1)2 + 4(1) - 8
= 1 + 1 + 2 + 4 - 8 = 0
(x - 1) is a factor of p(x).
Most Upvoted Answer
Direction: In the following questions, a statement of assertion (A) i...
Assertion: (x - 2) and (x - 1) are factors of the polynomial x^4 - x^3 + 2x^2 + 4x - 8.
Reason: For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0.
Explanation:
To determine whether the assertion and reason are true or false, let's analyze them separately:
Assertion: (x - 2) and (x - 1) are factors of the polynomial x^4 - x^3 + 2x^2 + 4x - 8.
This assertion can be tested by dividing the given polynomial by (x - 2) and (x - 1) using synthetic division or long division. If the remainder is zero in both cases, then the respective factors are indeed factors of the polynomial.
(x - 2):
Using synthetic division, we have:
2 | 1 -1 2 4 -8
| 2 2 8 24
-------------------
1 1 4 12 16
The remainder is 16, which is not zero. Therefore, (x - 2) is not a factor of the polynomial.
(x - 1):
Using synthetic division, we have:
1 | 1 -1 2 4 -8
| 1 0 2 6
-------------------
1 0 2 6 -2
The remainder is -2, which is not zero. Therefore, (x - 1) is not a factor of the polynomial.
Based on the above calculations, the assertion is false.
Reason: For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0.
This reason is false. A polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0, not p(a) ≥ 1. The statement in the reason is incorrect.
Conclusion:
From the analysis above, we can conclude that the assertion (A) is false and the reason (R) is false as well. Therefore, the correct answer is option (d) - Assertion (A) is false but reason (R) is true.
Reason: For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0.
Explanation:
To determine whether the assertion and reason are true or false, let's analyze them separately:
Assertion: (x - 2) and (x - 1) are factors of the polynomial x^4 - x^3 + 2x^2 + 4x - 8.
This assertion can be tested by dividing the given polynomial by (x - 2) and (x - 1) using synthetic division or long division. If the remainder is zero in both cases, then the respective factors are indeed factors of the polynomial.
(x - 2):
Using synthetic division, we have:
2 | 1 -1 2 4 -8
| 2 2 8 24
-------------------
1 1 4 12 16
The remainder is 16, which is not zero. Therefore, (x - 2) is not a factor of the polynomial.
(x - 1):
Using synthetic division, we have:
1 | 1 -1 2 4 -8
| 1 0 2 6
-------------------
1 0 2 6 -2
The remainder is -2, which is not zero. Therefore, (x - 1) is not a factor of the polynomial.
Based on the above calculations, the assertion is false.
Reason: For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0.
This reason is false. A polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) = 0, not p(a) ≥ 1. The statement in the reason is incorrect.
Conclusion:
From the analysis above, we can conclude that the assertion (A) is false and the reason (R) is false as well. Therefore, the correct answer is option (d) - Assertion (A) is false but reason (R) is true.
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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?
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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? 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 Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? 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 Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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Here you can find the meaning of Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : (x + 2) and (x - 1) are factors of the polynomial x4 + x3 + 2x2 + 4x - 8.Reason : For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 9 tests.
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