BASIC CONCEPTS IN ALGEBRA

Closure Property (Addition)

a + b = c ; all are real numbers

Closure Property (Multiplication)

a * b = d ; all are real numbers

Commutative Property (Addition)

a + b = b + a

Commutative

a + ( b + c) = (b + c) + a » _______ Property

Commutative Property (Multiplication)

a * b = b *a

Associative Property (Addition)

a + (b + c) = (a + b) + c

Associative Property (Multiplication)

a*(b*c) = (a*b)*c

Distributive Property

a*(b + c) = a*b + a*c

Additive Identity Property

a + 0 = a

Multiplicative Identity Property

a*1 = a

Additive Inverse Property

a + (-a) = 0

Multiplicative Inverse Property

a*(1/a) = 1

A * B = ?

GCF * LCM

Steps for LCM

Prime Factorization » [a^j * b^k * c^l ] ; highest exponent of the pair

Steps for GCF

Prime Factorization » [a^j * b^k * c^l ] ; lowest exponent of the pair

Quadratic Equation

x = [ -b + SQRT(b² - 4ac) ] / 2a

Discriminant

b² - 4ac

b² - 4ac < 0

Roots are Imaginary & Unequal

b² - 4ac = 0

Roots are Real, Rational & Equal » from a Perfect Square Trinomial

b² - 4ac > 0 & Perfect Square

Roots are Real, Rational & Unequal

b² - 4ac > 0 & NOT a Perfect Square

Roots are Real, Irrational & Unequal

Sum of Roots of the Quadratic Equation

Sum = -b/a

Product of Roots of the Quadratic Equation

Product = c/a

SUM and PRODUCT of Roots » Quadratic Equation

x² - SUM(x) + PRODUCT = 0

SUM of roots [r, s, t] of a Quadratic Equation

r + s +t = -b/a

Sum of Pairs Product of roots [r, s, t] of a Quadratic Equation

r*s + s*t + r*t = c/a

Product of roots [r, s, t] of a Quadratic Equation

r*s*t = -d/a