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NCERT Class 9 Mathematics Exercise Set 2.1 Solutions: Introduction to Linear Polynomials

Step-by-step working for every question of Exercise Set 2.1 in NCERT's Class 9 Mathematics book, chapter “Introduction to Linear Polynomials”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.

1. Ex 2.1 Q1

   Degree of each polynomial: (i) 2x² − 5x + 3, (ii) y³ + 2y − 1, (iii) −9, (iv) 4z − 3.

   1. (i) The highest power of x in 2x² − 5x + 3 is 2, so the degree is 2.
   2. (ii) The highest power of y in y³ + 2y − 1 is 3, so the degree is 3.
   3. (iii) The polynomial −9 is a constant, which can be written as −9x⁰, so the degree is 0.
   4. (iv) The highest power of z in 4z − 3 is 1, so the degree is 1.

   Answer: (i) 2; (ii) 3; (iii) 0; (iv) 1

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2. Ex 2.1 Q2

   Give one polynomial each of degree 1, 2 and 3.

   1. A polynomial of degree 1 is a linear polynomial with the highest power of the variable being 1.
   2. An example of a polynomial of degree 1 is 2x + 3.
   3. A polynomial of degree 2 is a quadratic polynomial with the highest power of the variable being 2.
   4. An example of a polynomial of degree 2 is 3x² − x + 4.
   5. A polynomial of degree 3 is a cubic polynomial with the highest power of the variable being 3.
   6. An example of a polynomial of degree 3 is 4x³ − 2x + 7.
   7. Any polynomial whose highest power is 1, 2 or 3 respectively is also a correct answer.

   Answer: Degree 1: 2x + 3; Degree 2: 3x² − x + 4; Degree 3: 4x³ − 2x + 7 (other answers are also correct)

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3. Ex 2.1 Q3

   In x⁴ − 3x³ + 6x² − 2x + 7, what are the coefficients of x² and of x³?

   1. Write the given polynomial as x⁴ − 3x³ + 6x² − 2x + 7.
   2. Identify the term containing x², which is 6x².
   3. The coefficient of x² is the number multiplying it, so it is 6.
   4. Identify the term containing x³, which is −3x³.
   5. The coefficient of x³ is the number multiplying it, so it is −3.

   Answer: coefficient of x² is 6; coefficient of x³ is −3

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4. Ex 2.1 Q4

   Coefficient of z in 4z³ + 5z² − 11.

   1. Identify the given polynomial as 4z³ + 5z² − 11.
   2. List the terms present in the polynomial: 4z³, 5z², and −11.
   3. Observe that there is no term containing z to the power of 1.
   4. Since the term z is missing, its coefficient is taken as 0.

   Answer: 0

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5. Ex 2.1 Q5

   Constant term of 9x³ + 5x² − 8x − 10.

   1. The given polynomial is 9x³ + 5x² − 8x − 10.
   2. The constant term is the term that does not contain the variable x.
   3. In this polynomial, the terms with x are 9x³, 5x², and −8x.
   4. The remaining term is −10, which has no variable attached to it.
   5. Therefore, the constant term is −10.

   Answer: −10

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