Master Mathematics
One Concept at a Time

Comprehensive self-learning resources for HKDSE.

Form 1

Simple Polynomials | 簡易多項式

Introduction to the language of Algebra. Learn how to identify terms, coefficients, and degrees.

REVISION MOVIE

Concept Summary

Watch & Listen

AI Generator

Infinite Practice

Unlimited questions. Topics follow the Concept Notes order.

Study Resources

Concept Notes (PDF)

Complete Chapter Summary with examples.

View & Print

Practice Quiz

Adaptive difficulty based on your progress.

Start

Revision Movie

1 / 20

Class Records

Student	Topic Mastery (Sub-topics)	Total Solved
Loading records...

Adaptive AI Arena

Topic 1: Indices

Streak: 0 🔥

Topic: Loading...

Loading question...

Chapter 10: Summary Notes

Chapter Summary: Manipulation of Simple Polynomials

1. Laws of positive integral indices

If $m$ and $n$ are positive integers, then:

(a) $a^m \times a^n = a^{m+n}$
(b) $a^m \div a^n = \frac{a^m}{a^n} = a^{m-n}$ (where $a \neq 0$ and $m > n$)

Example 1: Simplify $\frac{b^5 \times b^2}{b^3}$.
Solution: $\frac{b^{5+2}}{b^3} = \frac{b^7}{b^3} = b^{7-3} = b^4$

2. Monomials

A monomial is an algebraic expression with only one term (number, variable, or product).

(i) Coefficient: The numerical part.
(ii) Degree: The sum of indices of all variables.

Example 2: For $-5x^2y$:
Coefficient = $-5$
Degree = $2 + 1 = 3$

3. Polynomials

Sum of monomials. Example: $3x^2 - 5x + 7$.

(i) Terms: Each monomial in the polynomial ($3x^2$, $-5x$, $7$).
(ii) Constant term: The term with no variable ($7$).
(iii) Degree of polynomial: The highest degree among all terms ($2$).

4. Arrangement of terms

Consider polynomial $-2x + 5 + x^3$:
(a) Descending order (highest power first): $x^3 - 2x + 5$
(b) Ascending order (lowest power first): $5 - 2x + x^3$

5. Simplification

Combine Like Terms (terms with same variables and indices).

Example 3: Simplify $4a + 3b - 2a$.
Solution: $(4a - 2a) + 3b = 2a + 3b$

6. Value of a polynomial

Example 4: Find value of $2x^2 - 1$ when $x = 3$.
Solution: $2(3)^2 - 1 = 2(9) - 1 = 18 - 1 = 17$

7. Addition and Subtraction

Remove brackets and combine like terms. Watch the signs!

Example 5: $(3x + 2) - (x - 4)$
$= 3x + 2 - x + 4$
$= 2x + 6$

8. Multiplication

Use Distributive Law: $a(x+y) = ax + ay$.

Example 6: Expand $(x+2)(x+3)$
$= x(x+3) + 2(x+3)$
$= x^2 + 3x + 2x + 6$
$= x^2 + 5x + 6$

Master Mathematics
One Concept at a Time

Simple Polynomials | 簡易多項式

Concept Summary

Infinite Practice

Study Resources

Concept Notes (PDF)

Practice Quiz

Class Records

Adaptive AI Arena

Loading question...

Certificate of Achievement

Student Name

Chapter Summary: Manipulation of Simple Polynomials

1. Laws of positive integral indices

2. Monomials

3. Polynomials

4. Arrangement of terms

5. Simplification

6. Value of a polynomial

7. Addition and Subtraction

8. Multiplication

Master Mathematics One Concept at a Time

Simple Polynomials | 簡易多項式

Concept Summary

Infinite Practice

Study Resources

Concept Notes (PDF)

Practice Quiz

Class Records

Student Login

Adaptive AI Arena

Loading question...

Certificate of Achievement

Student Name

Chapter Summary: Manipulation of Simple Polynomials

1. Laws of positive integral indices

2. Monomials

3. Polynomials

4. Arrangement of terms

5. Simplification

6. Value of a polynomial

7. Addition and Subtraction

8. Multiplication

Master Mathematics
One Concept at a Time