numerical coefficients of, 320
operations on, 322–324, 329–332, 340–346
prime, 370
terms of, 321
trinomial, 321
inx, 321
Positive exponents, 305–306
Positive numbers, 28
Positive slope, 202
Positive square roots, 494
Power rules for exponents, 298–299
Powers, 15, 296
descending, 321
Price per unit, 130
Prime factors of a number, 3
Prime number, 2, 360
Prime polynomials, 370
Principal square root, 494
Product, 2, 49, 55
of the sum and difference of two
terms, 336
Product rule
for exponents, 296–297
for radicals, 504
Proper fraction, 2
Properties
of radicals, 509
of real numbers, 60–66
Proportion(s), 131
applications of, 133
cross products of, 131–132
extremes of, 131
means of, 131
solving, 133
terms of, 131
Pyramid, volume of, 127
Pythagorean theorem, 402, 497
proof of, 498, 503
Quadrants, 180
Quadratic equations, 324, 392, 554
applications of, 400, 565
completing the square method for
solving, 561
with complex number solutions, 578
factoring method for solving, 392, 554
with fractions, 571
graphing of, 324, 580
intercepts, 581
with no real solution, 556
with one solution, 570
quadratic formula method for solving,
568–569
square root method for solving, 555
standard form of, 392, 554
steps to solve, 394
steps to solve an applied problem, 400
steps to solve by completing the
square, 562
summary of solution methods, 573
Quadratic expression, 392
Quadratic formula, 568–569
discriminant of, 570
Quadratic formula method for solving
quadratic equations, 568–569
Quadratic functions, 583
domain of, 583
intercepts of, 584
range of, 583
Quadratic models, 403
Quotient, 5, 51, 55, 341
of opposites, 424
Quotient rule
for exponents, 306
for radicals, 507Radical, 494
Radical equations, 531
steps to solve, 533
Radical expressions, 494
guidelines for simplifying, 523
simplifying products of, 524
squaring of, 495
summary of simplifying, 518
using conjugates to rationalize
denominators of, 525–526
writing quotients in lowest terms, 527
Radical symbol, 494
Radicals, 494
conjugates of, 525
equations with, 531
index of, 499
like, 513
operations on, 504, 507, 513
order of, 499
product rule for, 504
properties of, 509
quotient rule for, 507
simplified form of, 505, 507, 518
simplifying, 505, 507
simplifying other roots, 509
simplifying using rational exponents, 542
unlike, 513
with variables, 508
Radicand, 494
Range, 229, 232
of a quadratic function, 583
Rate of change, 209
Rate of work, 469
Ratio, 130
from word phrases, 130
Rational expressions, 420
applications of, 467
with denominator zero, 421
equations with, 456
equivalent forms for, 424–425
evaluating, 420
fundamental property of, 422
in lowest terms, 421
with numerator zero, 421operations on, 429–430, 440–441, 443
solving an equation with, 457–458
steps for division of, 432
steps for multiplication of, 432
summary of operations on, 465–466
undefined values for, 421
Rational numbers, 29–30
graph of, 29
using as exponents, 540
Rationalizing denominators, 517, 526
Reading graphs, 176
Real numbers, 30.See alsoNumbers
absolute value of, 32–33
additive inverse of, 31–32
operations on, 37–40, 49–52
opposites of, 31–32
order of operations of, 40–41, 53
ordering of, 31
properties of, 60–66
sets of, 30
summary of operations on, 59
Real part of a complex number, 575
Reciprocals, 51, 63
Reciprocals of fractions, 5, 51, 63
Rectangular box, volume of, 126
Rectangular coordinate system, 180
Region of a graph, 224–225
Relation, 229
domain of, 229
range of, 229
Richter, Charles F., 315
Richter scale, 315
Right angle, 113
Right triangle, 402
hypotenuse of, 402
legs of, 402
Rise, 199
Roots
cube, 499, 520
fourth, 499
negative, 494, 500
nth, 499
positive, 494, 500
principal, 494, 500
square, 494, 496
Rules for exponents, 307
Run, 199Scatter diagram, 182
Scientific notation, 312
on calculators, 317
and exponents, 312
steps to write a number in, 312
Second-degree equation.SeeQuadratic
equations
Semiperimeter, 539
of a triangle, 539
Set(s), 25, 597
complement of, 599
elements of, 25, 597S
R
Q
Index I-5