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
(x+y)2=x2+2xy+y2
Example: (3+2)2=9+12+4=25 ✓
(x−y)2=x2−2xy+y2
Example: (5−2)2=25−20+4=9 ✓
(x+y)(x−y)=x2−y2
Example: (7+3)(7−3)=49−9=40 ✓
(x+a)(x+b)=x2+(a+b)x+ab
Example: (x+3)(x+5)=x2+8x+15 ✓
(x+y+z)2=x2+y2+z2+2xy+2yz+2zx
(x+y)3=x3+y3+3xy(x+y)
Expanded: =x3+3x2y+3xy2+y3
(x−y)3=x3−y3−3xy(x−y)
Expanded: =x3−3x2y+3xy2−y3
x3+y3+z3−3xyz=(x+y+z)(x2+y2+z2−xy−yz−zx)
Special Case: If x+y+z=0, then x3+y3+z3=3xyz!