Q1. Page 18: Find the degrees of the following polynomials: (i) 2x² - 5x + 3 (ii) y³ + 2y - 1 (iii) -9 (iv) 4z - 3
Answer:
(i) 2x² - 5x + 3: The highest power of x is 2. Degree = 2 (Quadratic).
(ii) y³ + 2y - 1: The highest power of y is 3. Degree = 3 (Cubic).
(iii) -9: This is a constant. Degree = 0 (Constant polynomial).
(iv) 4z - 3: The highest power of z is 1. Degree = 1 (Linear).
Q2. Page 18: Write polynomials of degrees 1, 2 and 3.
Answer:
Degree 1 (Linear): 2x + 3, 5y - 7, z + 1
Degree 2 (Quadratic): x² - 4x + 4, 2y² + y - 1, z² + 5
Degree 3 (Cubic): x³ + 2x² - x + 1, y³ - 2y² + 5y - 3, z³ + 1
Q3. Page 18: What are the coefficients of x² and x³ in the polynomial x⁴ - 3x³ + 6x² - 2x + 7?
Answer:
In the polynomial x⁴ - 3x³ + 6x² - 2x + 7:
- Coefficient of x² is 6.
- Coefficient of x³ is -3.
Q4. Page 19: What is the coefficient of z in the polynomial 4z³ + 5z² - 11?
Answer:
The coefficient of z in 4z³ + 5z² - 11 is 0 (since there is no term with z¹).
Q5. Page 19: What is the constant term of the polynomial 9x³ + 5x² - 8x - 10?
Answer:
The constant term of 9x³ + 5x² - 8x - 10 is -10.