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📐 Chapter 2: Introduction to Linear Polynomials • Exercise Set 2.1

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Exercise Set 2.1 5Exercise Set 2.2 7Exercise Set 2.3 5Exercise Set 2.4 4Exercise Set 2.5 3Exercise Set 2.6 1End-of-Chapter Exercises 14All Exercises 39
Q1

Exercise Set 2.1

1. Find the degrees of the following polynomials:

(i) 2x² - 5x + 3      (ii) y³ + 2y - 1      (iii) -9      (iv) 4z - 3

  • (i) 2x² - 5x + 3: The highest power of the variable x is 2, so the degree is 2.
  • (ii) y³ + 2y - 1: The highest power of the variable y is 3, so the degree is 3.
  • (iii) -9: This is a non-zero constant polynomial (can be written as -9x⁰). Its degree is 0.
  • (iv) 4z - 3: The highest power of the variable z is 1, so the degree is 1.
Q2

Exercise Set 2.1

2. Write polynomials of degrees 1, 2 and 3.

Here are examples of polynomials with the specified degrees:

  • Degree 1 (Linear): 5x + 2
  • Degree 2 (Quadratic): 3y² - 4y + 7
  • Degree 3 (Cubic): 2z³ + z² - 8z + 1
Q3

Exercise Set 2.1

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

  • The term containing x² is +6x², so the coefficient of x² is 6.
  • The term containing x³ is -3x³, so the coefficient of x³ is -3.
Q4

Exercise Set 2.1

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

The polynomial 4z³ + 5z² - 11 does not contain a term with z to the power of 1. It can be written as 4z³ + 5z² + 0z - 11. Therefore, the coefficient of z is 0.

Q5

Exercise Set 2.1

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

The constant term is the term that does not contain any variable. In the polynomial 9x³ + 5x² - 8x - 10, the constant term is -10.