Exercise 2.1 Class 9 Maths Solutions | Introduction to Linear Polynomials (Ganita Manjari)

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Exercise 2.1 introduces the basic concepts of polynomials, including finding the degree, identifying coefficients, and understanding constant terms. This exercise forms the foundation for algebra in higher classes. Below are clear and step-by-step solutions for all questions.

Exercise 2.1 Solutions

✅ Question 1

Find the degrees of the following polynomials:

✏️ Solution

(i) 2x²−5x+3
👉 Highest power of x=2
So Degree = 2

(ii) y³+2y−1
👉 Highest power of y=3
So Degree = 3

(iii) −9
👉 This is non zero Constant polynomial
So Degree = 0

(iv) 4z−3
👉 Highest power of z=1
So Degree = 1

✅ Question 2

Write polynomials of degrees 1, 2, and 3.

✏️ Solution

Examples:

  • Degree 1 (Linear polynomial):

7x+5

  • Degree 2 (Quadratic polynomial):

x²−7x+1

  • Degree 3 (Cubic polynomial):

x³+2x²−x+4

✔ NOTE: Students may also provide other valid examples, and those will be accepted as well.

✅ Question 3

What are the coefficients of x² and x³ in the polynomial
x⁴−3x³+6x²−2x+7?

✏️ Solution

  • Coefficient of x²=6
  • Coefficient of x³=−3

✅ Question 4

What is the coefficient of z in the polynomial
4z³+5z²−11?

✏️ Solution

Since there is no z term in the polynomial.

So Coefficient of z=0

✅ Question 5

What is the constant term of the polynomial
9x³+5x²−8x−10?

✏️ Solution

👉 Constant term is the  term without variable

So Constant term is  -10

🟢 Conclusion

This exercise helps students clearly understand:

  • Degree of a polynomial
  • Coefficients of terms
  • Constant terms

These basics are essential for solving algebraic problems in higher classes.

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