Easy Algebra Step-by-Step

Index 245

diagram of, 172f
distance between two, 176–177
equa l, 173 –174
a line through two
parallel line to, 181
perpendicular line to, 181–182
point-slope equation for, 190–193
slope of, 178–181
slope y-intercept equation for, 184–190
midpoint between two, 177
i n quad ra nt s, 174 –17 5
from x-y T-table, 185 –186
Polynomials
addition of, 90–91
binomials. See Binomials
defi nition of, 85
dividing, 110–117, 120
factoring, 119–137
identifying, 86
monomials. See Monomials
multiplying, 94 –102
in polynomial expressions, 104–105
in rational expressions, 139
simplifying, 91, 119–120
subtraction of, 92–93
trinomials. See Tr inomia ls
Polynomial expressions, 104–109
Positive integer, 3, 3f
Positive numbers
absolute value of, 16–17
addition of, 17–19
categorization of, 7
cube of, 36, 45
cube root of, 7, 36–39
in division, 29–30
exponentiation of
with fractions, 53–57
with natural numbers, 44–48
with negative numbers, 50–52
with one, 45
with zero, 49
fourth root of, 38
integers, 3, 3f
multiplication of, 26–28
natural. See Natural numbers
nth root of, 38
on number line, 3–4, 3f, 6, 160f
sign for, 3
square of, 32, 45

square roots of, 5, 7, 32–35, 39–42

subtraction of, 21–24

whole. See Whole numbers

Power of a difference rule, 80, 81, 220

Power of a product rule, 78–80, 119–120

Power of a quotient rule, 79

Power of a sum rule, 80, 81, 119–120, 220

Power to a power rule, 77–78

Prime factor, 148

Principal cube root, 36–37, 39, 53

Principal nth root of a, 38–39

Principal square root, 32–36, 38, 53, 164

Product rule, 74–75, 81

Quadratic equations, 127–133, 163–169

Quadratic function, 201, 202f

Quotient rule, 75–77, 81

Radicals, 38–42

Radicand, 38

Range of functions, 195 –196, 197

Rational expressions

algebraic fractions. See Algebraic fractions

defi nition of, 139

fundamental principles of, 139–143

Rational numbers

decimal form of, 4–5

defi nition of, 4

integers, 3–5, 3f, 6f

negative. See Negative numbers

nonintegers, 6

positive. See Positive numbers

set of, 4

Real numbers

absolute value of, 15–17

addition rules for signed, 17–20

categorization of, 64

comparing, 14–15

defi nition of, 6

division rules for signed, 29–30

in domain of functions, 196–199

fi eld properties of, 8–12

graph of, 8

irrational, 5–6, 6f

multiplication rules for signed, 26–28

nth root of, 38

on number line, 6, 6f, 8

rational. See Rational numbers

subtraction rules for signed, 21–25