Unit 9 Class 11 Math Notes – Division of Polynomials (Punjab Board New Book)
Unit 9 (Chapter 9) Class 11 Math Notes – Division of Polynomials: step-by-step solutions of Exercise 9.1 and Exercise 9.2 for the Punjab Board new book (1st Year). Tap an exercise below to open its PDF solution, then view it online or download it.
This unit is part of our Class 11 maths notes for the Punjab Board new book, where you can open the solutions of the other units.
Exercise Wise Solutions of Unit 9 Class 11 Math
What Each Exercise of Unit 9 Covers
Exercise 9.1 – Division, Remainder and Factor Theorems
Exercise 9.1 has 10 questions on long division, the remainder theorem, the factor theorem and synthetic division, including finding unknown constants such as \(p\), \(q\) and \(k\).
Exercise 9.2 – Applications of Polynomial Division
Exercise 9.2 has 7 questions on applications: prediction error of polynomial models, and zeros, poles and stability of transfer functions.
Key Formulas of Unit 9 Class 11 Math
- Division: \(f(x)=\text{divisor}\cdot q(x)+R(x)\).
- Remainder theorem: the remainder of \(f(x)\) divided by \(x-a\) is \(f(a)\).
- Factor theorem: \(x-a\) is a factor of \(f(x)\) if and only if \(f(a)=0\).
- A transfer function is stable if all its poles satisfy \(|z|<1\).
Related Class 11 Math Notes
Continue with Unit 8 Class 11 Math Notes and Unit 10 Class 11 Math Notes, or go back to the Class 11 maths notes hub for all 14 units.
FAQs About Unit 9 Class 11 Math
How many exercises are there in Unit 9?
Unit 9 has two exercises: Exercise 9.1 and Exercise 9.2.
When is synthetic division used?
Synthetic division is a short way to divide a polynomial by a linear factor such as \(x-a\). It gives the quotient and the remainder without writing the full long division.
Are these notes for the new book?
Yes. These solutions are for the new Class 11 mathematics book by PECTAA (2025 edition onwards), used by the nine BISE Punjab boards: Lahore, Gujranwala, Faisalabad, Multan, Rawalpindi, Sargodha, Sahiwal, Bahawalpur and Dera Ghazi Khan.