Assertion Reason Questions For Class 9 Maths Chapter 2 Introduction To Linear Polynomials

Assertion-reason questions for Class 9 Maths Chapter 2, Introduction to Polynomials, are available in this Maths article. These questions are very useful for understanding the chapter and solving problems with confidence. The article helps students revise important concepts such as terms and coefficients of polynomials, types of polynomials, degree of a polynomial, monomials, binomials, trinomials, value of a polynomial, and algebraic identities. Our subject experts have provided detailed solutions based on the CBSE syllabus and the NCERT textbook. This study material helps students strengthen their conceptual understanding, practise important question types, and perform well in examinations. A free downloadable PDF is also available for quick revision and practice.

Assertion and Reason Questions on Introduction to Polynomials for Class 9

Directions: In each question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

• (a) Both A and R are true, and R is the correct explanation of A.
• (b) Both A and R are true, but R is not the correct explanation of A.
• (c) A is true but R is false.
• (d) A is false but R is true.

Q1:
Assertion (A): x²+2x+1 is a polynomial in one variable.
Reason (R): An algebraic expression in which the exponents of the variable are whole numbers (non-negative integers) is called a polynomial.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (A)
Explanation: A is true because x²+2x+1 has only whole-number powers of x. R is also true because it gives the correct definition of a polynomial. Since R explains A, option (A) is correct.

Q2:
Assertion (A): A polynomial of degree nn has exactly n zeroes.
Reason (R): A linear polynomial has exactly one zero.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (D)
Explanation: A is false because a polynomial of degree nn has at most nn zeroes, and over the real numbers it may have fewer. For example, x²+1 has degree 2 but no real zeroes. R is true because a linear polynomial ax+b (a≠0) always has exactly one real zero: x=−b/a.

Q3:
Assertion (A): If p(2)=0 for a polynomial p(x), then (x−2) is a factor of p(x).
Reason (R): The Remainder Theorem states that when p(x) is divided by (x−a), the remainder is p(a).

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (B)
Explanation: A is true because it states the Factor Theorem. R is also true because it correctly states the Remainder Theorem. However, R does not explain A, so option (B) is correct.

Q4:
Assertion (A): 1/x is a polynomial of degree −1.
Reason (R): An expression with a negative integer exponent on the variable is not a polynomial.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (D)
Explanation: A is false because 1/x =  x−1 has a negative exponent, so it is not a polynomial. R is true because polynomials can only have non-negative integer powers of xx. Hence, option (D) is correct.

Q5:
Assertion (A): x²+5x+6 can be factorised as (x+2)(x+3).
Reason (R): To factorise x²+bx+c, find two numbers whose sum equals b and whose product equals c.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (C)
Explanation: A is true because (x+2)(x+3)=x²+5x+6. R is false because the correct rule is sum=b and product=c, not the other way around. Hence, option (C) is correct.

Q6:
Assertion (A): The degree of p(x)+q(x), where p(x)=3x⁴−x² and q(x)=−3x⁴+2x, is 2.
Reason (R): The sum of two polynomials is also a polynomial.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (B)
Explanation: A is true because p(x)+q(x)=−x²+2x, which has degree 2 after cancellation. R is also true because polynomials are closed under addition. However, R does not explain the degree change in A, so option (B) is correct.

Q7:
Assertion (A): When p(x)=x³−6x²+2x−4 is divided by (x−1), the remainder is −7.
Reason (R): The Remainder Theorem states that when p(x) is divided by (x−a), the remainder equals p(a).

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (A)
Explanation: A is true because p(1)=1−6+2−4=−7. R is true and correctly explains A, since the Remainder Theorem tells us to substitute x=1, which gives the remainder as p(1)=−7.

Q8:
Assertion (A): The value of p(x)=2x²−x+3 at x=−1 is 6.
Reason (R): The value of a polynomial p(x) at x=a is obtained by substituting 'a' in place of 'x'.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (A)
Explanation: A is true because p(−1)=2(−1)²−(−1)+3=2+1+3=6. R is true and explains A because it gives the method used to find p(−1), and applying it gives 6.

Q9:
Assertion (A): (x+2) is a factor of p(x)=x³+2x²−x−2.
Reason (R): (x−a) is a factor of p(x) if p(x)=0 for all values of x.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (C)
Explanation: A is true because p(-2)=0, so (x+2)(x+2) is a factor. R is false because the Factor Theorem applies to a specific value of 'a', not to all values of 'x'. Hence, option (C) is correct.

Q10:
Assertion (A): 2x²+3x²+3x is a binomial.
Reason (R): A polynomial with exactly two terms is called a binomial.

Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is not the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.

Answer: Option (A)
Explanation: A is true because 2x²+3x²+3x has exactly two terms: 2x² and 3x. R is true and explains A because any polynomial with exactly two terms is a binomial.

Download free PDF of Assertion and Reasoning Questions for Class 9 Maths Chapter 2 -  Introduction to Polynomials

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Assertion and Reason Questions on Introduction to Polynomials for Class 9