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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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.
Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0
- 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 'A'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of assertion (A) i...
P(x) = x3 + 3x2 + 5x + 6
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g(x) = x + 2
x = -2
put x = -2 in p(x)
p(-2) = (-2)3 + 3(-2)2 + 5(-2) + 6
= -8 + 12 - 10 + 6
= 0
since p(x) is zero
X + 2 is a factor of x3 + 3x2 + 5x + 6
Checking
let x = -2 q(x) = 2x + 4
q(-2) = 2(-2) + 4
= -4 + 4
= 0
since reminder is zero
x + 2 is a factor of 2x + 4
Most Upvoted Answer
Direction: In the following questions, a statement of assertion (A) i...
Assertion: (x - 2) is a factor of x^3 - 3x^2 - 5x - 6 and of 2x - 4.
Reason: If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0.
The given assertion and reason are both true and the reason is the correct explanation of the assertion.
Explanation:
To prove that the given assertion is true, we need to show that (x - 2) is a factor of both x^3 - 3x^2 - 5x - 6 and 2x - 4.
Factor of x^3 - 3x^2 - 5x - 6:
To check if (x - 2) is a factor of x^3 - 3x^2 - 5x - 6, we can use synthetic division or long division method. Let's use synthetic division.
2 | 1 -3 -5 -6
| 2 -2 -14
|__________________
1 -1 -7 -20
The remainder is 0, which means (x - 2) is a factor of x^3 - 3x^2 - 5x - 6.
Factor of 2x - 4:
To check if (x - 2) is a factor of 2x - 4, we can substitute x = 2 in the polynomial.
2(2) - 4 = 4 - 4 = 0
Since the polynomial evaluates to 0 when x = 2, (x - 2) is a factor of 2x - 4.
Reason:
The reason provided states that if p(x) is a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x) if p(a) = 0. This is a well-known property of polynomials.
In this case, p(x) = x^3 - 3x^2 - 5x - 6 and a = 2. When we substitute a = 2 in p(x), we get:
p(2) = (2)^3 - 3(2)^2 - 5(2) - 6
= 8 - 12 - 10 - 6
= 0
Since p(2) = 0, according to the property stated in the reason, (x - 2) is a factor of p(x).
Therefore, both the assertion and reason are true and the reason is the correct explanation of the assertion. Hence, the correct answer is option A.
Reason: If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0.
The given assertion and reason are both true and the reason is the correct explanation of the assertion.
Explanation:
To prove that the given assertion is true, we need to show that (x - 2) is a factor of both x^3 - 3x^2 - 5x - 6 and 2x - 4.
Factor of x^3 - 3x^2 - 5x - 6:
To check if (x - 2) is a factor of x^3 - 3x^2 - 5x - 6, we can use synthetic division or long division method. Let's use synthetic division.
2 | 1 -3 -5 -6
| 2 -2 -14
|__________________
1 -1 -7 -20
The remainder is 0, which means (x - 2) is a factor of x^3 - 3x^2 - 5x - 6.
Factor of 2x - 4:
To check if (x - 2) is a factor of 2x - 4, we can substitute x = 2 in the polynomial.
2(2) - 4 = 4 - 4 = 0
Since the polynomial evaluates to 0 when x = 2, (x - 2) is a factor of 2x - 4.
Reason:
The reason provided states that if p(x) is a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x) if p(a) = 0. This is a well-known property of polynomials.
In this case, p(x) = x^3 - 3x^2 - 5x - 6 and a = 2. When we substitute a = 2 in p(x), we get:
p(2) = (2)^3 - 3(2)^2 - 5(2) - 6
= 8 - 12 - 10 - 6
= 0
Since p(2) = 0, according to the property stated in the reason, (x - 2) is a factor of p(x).
Therefore, both the assertion and reason are true and the reason is the correct explanation of the assertion. Hence, the correct answer is option A.
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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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. 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) is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.Reason : If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0a)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 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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