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Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.
Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)
and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,
where r(x) = 0 of degree of r(x)
Verified Answer
Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) an...
The assertion (A) is false, and the reason (R) is true.
The equation 3x^2 + x - 1 = (x + 1)(3x - 2x) + 1 is not true, as the left-hand side is a second-degree polynomial and the right-hand side is not equivalent to it.
However, the reason (R) is true. The statement is a special case of the Euclidean division algorithm, which states that if p(x) and g(x) are two polynomials such that the degree of p(x) is greater than or equal to the degree of g(x) and g(x) is not equal to 0, then there exist unique polynomials q(x) and r(x) such that p(x) = g(x)q(x) + r(x), where the degree of r(x) is less than the degree of g(x), and r(x) is either equal to 0 or has a leading coefficient different from 0.
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) an...
Explanation:

Assertion (A):
3x^2 + x - 1 = (x + 1)(3x - 2x) + 1.

Reason (R):
If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree of r(x).

Explanation:
- When we expand the right side of the equation in the assertion, we get:
(x + 1)(3x - 2x) + 1 = (3x^2 - 2x + 3x - 2) + 1
= 3x^2 + x - 1
- Therefore, the assertion is true.

Explanation of Reason:
- If the degree of p(x) is greater than or equal to the degree of g(x), we can perform polynomial division to find q(x) and r(x) such that p(x) = g(x) q(x) + r(x).
- Here, q(x) is the quotient and r(x) is the remainder.
- Since the degree of g(x) is greater than or equal to 0, the remainder r(x) will have a degree less than the degree of g(x) or it could be zero.
- This process is known as polynomial division and is a fundamental concept in algebra.

Conclusion:
The assertion is true and the reason explains the concept of polynomial division when the degree of the divisor is greater than or equal to 0. This concept is essential in understanding polynomial operations and factorization.
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Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,where r(x) = 0 of degree of r(x)
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Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,where r(x) = 0 of degree of r(x) 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 Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,where r(x) = 0 of degree of r(x) covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,where r(x) = 0 of degree of r(x) .
Solutions for Assertion (A): 3x2 + x – 1 = (x + 1)(3x – 2x) + 1.Reason(R) If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x)and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) ,where r(x) = 0 of degree of r(x) in English & in Hindi are available as part of our courses for Class 9. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
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