Introduction to Number Systems
ch1-introduction
Rational Numbers
ch1-rational-numbers
Exercise 1.1 - Detailed Solutions
ch1-exercise-1-1
Irrational Numbers
ch1-irrational-numbers
Exercise 1.2 - Detailed Solutions
ch1-exercise-1-2
Real Numbers & Decimal Expansions
ch1-real-decimals
Exercise 1.3 - Detailed Solutions
ch1-exercise-1-3
Operations on Real Numbers
ch1-operations
Rationalizing the Denominator
ch1-rationalization
Exercise 1.4 & 1.5 - Solutions
ch1-exercise-1-4-5
Laws of Exponents for Real Numbers
ch1-laws-exponents
Chapter 1 Summary
ch1-summary
What is a Polynomial?
ch2-introduction
Types of Polynomials
ch2-types
Zeroes of a Polynomial
ch2-zeroes
Exercise 2.1 - Detailed Solutions
ch2-exercise-2-1
Remainder Theorem
ch2-remainder-theorem
Factor Theorem
ch2-factor-theorem
Algebraic Identities
ch2-identities
Exercise 2.4 - Identity Applications
ch2-exercise-2-4
Chapter 2 Summary
ch2-summary
| By Terms | By Degree |
|---|---|
| Monomial (1) | Constant (0) |
| Binomial (2) | Linear (1) |
| Trinomial (3) | Quadratic (2) |
| Cubic (3) |
| Theorem | Statement | Use |
|---|---|---|
| Remainder | Remainder = p(a) | Quick division |
| Factor | (x−a) is factor iff p(a)=0 | Finding factors |
| # | Identity |
|---|---|
| 1 | (x+y)2=x2+2xy+y2 |
| 2 | (x−y)2=x2−2xy+y2 |
| 3 | (x+y)(x−y)=x2−y2 |
| 4 | (x+a)(x+b)=x2+(a+b)x+ab |
| 5 | (x+y+z)2=x2+y2+z2+2xy+2yz+2zx |
| 6 | (x+y)3=x3+y3+3xy(x+y) |
| 7 | (x−y)3=x3−y3−3xy(x−y) |
| 8 | x3+y3+z3−3xyz=(x+y+z)(...) |
If x+y+z=0: x3+y3+z3=3xyz
🎉 Chapter 2 Complete!
Interactive Visualization