Binomials defined, 13 division by, FOIL method and, 22 multiplying binomial by trinomial,

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1 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-1 Index Absolute value defined, 46 functions and, Absolute value equations, solutions, Absolute value inequalities, solutions, Acceleration, 292 Addition of complex numbers, of functions, 151 of matrices, of polynomials, 13 of radical expressions, 7 of rational expressions, Addition method systems of equations, , 521, , 621 systems of nonlinear equations, 712, Additive identity, 187 Additive identity for matrices, 573 Additive inverse, 43, 187 Additive inverse for matrices, Amortization Formula, defined, 447 Annual Compound Interest Formula, defined, 432 Annuity Formula, defined, 442 Area of square formula, Arithmetic General Formula, defined, 739 Arithmetic sequences, defined, 738 Arithmetic series, 755 Asymptotes defined, 348 finding, horizontal asymptotes, of hyperbolas, 689, 692 linear asymptotes, 353 oblique asymptotes, quadratic asymptotes, 355 vertical asymptotes, Augmented matrices, 617, 618, 619, 620 Average rate of change, Average rate of change formula, Axis of symmetry defined, 662 of parabolas, , 664 Base Change of Base Formula, logarithmic functions and, Big Picture, concepts of, 41 44, 45 Binomials division by, FOIL method and, 22 multiplying binomial by trinomial, 14 special binomials, 24 25, 226 Binomial squared formula, 14 Binomial squares, 701 Central box, of hyperbolas, 689 Certain events, 777 Change of Base Formula, defined, 407 Circles as conic sections, 660, defined, 679 general form of, 705 identifying, 699 solutions, as special ellipses, Coefficient matrix, 603, 605, 617 Coefficients correlation coefficient, general form of a conic and, 699 Cofactors, 597 Collaborative activities exponential functions, 392 factoring techniques, finding equations, function review, graphing techniques, 78 identifying conics, 710 inverse functions, 202 linear equations, 51, loans and mortgages, logarithmic and exponential equations, multiplicative inverses of matrices, operations on functions, parabolas versus ellipses, polynomial functions, 299 properties of matrices, property of logarithms, rational functions, sequences, solving inequalities graphically, 275 solving quadratic equations, theoretical versus empirical probability, Combinations counting theory and, defined, 766 Combinations Formula, defined, 766 Common differences arithmetic sequences and, 739, 742 common ratios versus, polynomials and, , 291, , 294 slope of line and, 497 tables and, 291, , , 382, 383, 384 Common logarithms, 407 Common ratios common differences versus, geometric sequences and, 740, 741, 742 tables and, 381, 382, 383, 384 Commutative property of multiplication, 577, 591 Complement formulas for, 781 probability and, Completing the square, , Complex Conjugate Zeros Theorem, 340 defined, 338 Complex fractions defined, 35 simplification of, Complex numbers addition and subtraction of, defined, 217 definition of i and, division of, fractals and, multiplication of, Composed functions defined, 158 domain and range of, real-valued solutions and, 159 Composition, of functions, , Compound Interest Formula, defined, 433 Compression, , 666 defined, 318 Concave down graphs, 137 Concave up graphs, 137 Conic sections circles, 660, , 710 distance formula and, ellipses, 660, general form of conics, hyperbolas, 660, identifying conics, , 710 parabolas, 660, types of, 660 Conjugate axis, of hyperbolas, 689 Conjugates, 219 Consistent systems of equations, 515, 517 Constant denominators, 251 Constant matrix, 603, 617 Constant of variation, A-14, A-15 Constant polynomials, , 294, 302 Constants, exponential and logarithmic systems, Constraints, A-7, A-8 Continuous Compound Interest Formula, defined, 434 Continuous polynomials, 300, 301 Contradiction, 45 Correlation coefficient, Counting principle counting theory and, , 764, 766 defined, 761 Counting theory combinations and, counting principle, , 764, 766 permutations and, Covertices of ellipses, 673 of hyperbolas, 689 Cramer s Rule, Cube roots, 58 Cubic function models, 546, 549, 552 Curve of best fit, 530, 532, Cyclic behavior, 217 Data analysis appropriate models and, determination of good models, linear models and, modeling with graphing calculator and, systems of two-variable equations and, Decay applications of, , Decibels, Decreasing functions, 136, 137, 138 Defined area, 221 Degenerate cases, 705 Degree of a polynomial, defined, 13 Degrees, Demand function, 504 Denominators constant denominators, 251 least common denominator, 34, 251 rationalization of, 6, 8 9 I-1

2 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-2 I-2 Index Denominators (continued) single variable term in, variables in, Dependent systems of equations, , 519 Dependent variables defined, 107 functions and, 108, 109, Descending order, Determinants Cramer s Rule and, defined, 596 matrices and, Difference of two cubes formula, 24 Difference of two squares formula, 14, 24 Difference quotient, Dimension fractional dimension, 222 of matrices, , , 579 Directrix, of parabolas, 661, 662, 664 Direct variation, A-14 A-15 defined, A-14 Distance formula defined, 661 parabolas and, 662 Pythagorean Theorem and, Distinguishable permutations, Distributive property, 218 Dividends, defined, 16 Division of complex numbers, of functions, 151 of polynomials, 15 17, , 617 of rational expressions, 33 Divisors, defined, 16 Domain of combined functions, 153, 154 of composed functions, defined, 120 of functions, , of square roots, 123, Domain of all real numbers, 123, 124 Dominating terms, 350 e defined, natural logarithms and, 407 Equations. See also Systems of equations absolute value equations, Big Picture and, exponential equations, , , flow charts for solving, fractional exponent equations, linear equations, 41 46, 51, , logarithmic equations, , matrix equations, quadratic equations, , quadratic-like equations, square root equations, , 248 without solution or with many solutions, Even functions, 308 Even-power polynomials, 305 Events certain events, 777 defined, 776 impossible events, 777 independent events, 778 mutually exclusive events, 779 Expansion about a row or column, 597 Exponential decay, Exponential equations factoring and, greatest common factor and, solutions, Exponential expressions, 2 3 Exponential function models, 532, 535, 538, 547, 549, 551, Exponential functions basic characteristics of, , construction of, defined, 395 finding, , 524 geometric sequences and, 740 growth and decay, inverse of, nature of, number e and, Exponential growth, Exponential notation, 2 3 defined, 2 Exponents exponential notation, 2 3 fractional exponents, 4 6, logarithms and, Extraneous solutions, 242 Factorials defined, 733 simplification of, 767 Factoring combination of factoring techniques, 26 exponential equations and, by greatest common factor, 20 21, 226 by grouping, 25 26, 226 polynomials, quadratic equations and, special binomials, trinomials, 21 23, 226 Factor Theorem, defined, 330 Feasible region, A-8 Finite sequences, 732 Flipping translations, Focus, of parabola, 661, FOIL method, 14, 21 23, 218 Form of horizontal line, 499 Form of vertical line, 499 Formulas Amortization Formula, Annual Compound Interest Formula, 432 Annuity Formula, area of square, Arithmetic General Formula, 739 average rate of change formula, binomial squared formula, 14 Change of Base Formula, Combinations Formula, 766 combining functions and, 157 complement, 781 composed functions and, Compound Interest Formula, 433 Continuous Compound Interest Formula, 434 difference of two cubes formula, 24 difference of two squares formula, 14, 24 difference quotient formula, for ellipses, Fahrenheit-Celsius conversion formula, , 121, 170, 195, as functions, , , 125 Geometric General Formula, 741 for hyperbolas, 689 for inverse, 598 of lines, mutually exclusive events, 779 non-mutually exclusive events, 779 for nth partial sum of arithmetic series, 755 for nth partial sum of geometric series, 757 for parabolas, , 665 for permutations, 764 ph Formula, quadratic formula, , for sequences, series, 754 slope formula, , , for sum of infinite geometric series, 758 sum of two cubes formula, 24 Fractals, Fractional dimension, 222 Fractional exponents defined, 4 radicals and, 6 simplifying expressions with, 5 solutions of fractional exponent equations, Fractions complex fractions, functions in fractional form, 126 Functions. See also Polynomials application of composition, application of function operations, , combining functions, , composition of, , compound interest and, defined, 102, 120 dependent variables and, 108, 109, difference quotient and average rate of change, exponential functions, , , 521, , 524 formulas as, , , 125 fractals and, function notation, , increasing and decreasing functions, interval notation, 127 inverse functions, , 202, 398 linear functions, 125, 288, , 293, 294, logarithmic functions, , 521, , 524 maximums and minimums of,

3 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-3 Index I-3 non-quadratic functions, odd functions, one-to-one functions, , operations on, piecewise-defined functions, 84 87, rational functions, , relations and, , , 665 translating functions, , 665 Gaussian elimination applications and, 633 augmented matrices and, 617 Gaussian method, , General Form of a Conic, defined, 699 observations about, Geometric General Formula, defined, 741 Geometric sequences, defined, 740 Geometric series, Geometry area as function of perimeter, area of circle, 180, 186, 214, A-18 area of rectangular poster, 185 area of right triangle, 184 area of square, 110, circumference of circle, 180, 210 dimensions of box, 347 expansion of cubed figure, 201 volume of box, 135, , 182, 237, 238, 239 volume of cone, 210 volume of conical water tank, 184 volume of cube, 117, 118, 180, 186 volume of cylinder, 182 volume of sphere, 117, 118, 180, A-18 volume of water in water tank, 182 Graphing calculators. See also TI-83/84; TI-86 absolute value and, 59 absolute value inequalities and, approximating zeros using, basic commands, brightness of screen (contrast), 53 calculator keys, 52 combinations of translations and, complements and, conics in general form and, 706 determinants and, ellipses and, ENTER key, 53, 76 and exponential functions, 394 finding a graph, FRAC key, 59 functions and, Gaussian elimination and, 616, graphing with, Home Screen, 54 hyperbolas and, inverse of matrices and, local maximums and minimums and, logarithmic functions and, 407 matrices and, minus sign key, MODE key, 53 modeling with, MODE menu, 53 MORE key, 53 negative sign key, ON key, 52, 76 order of operations and, 52, 55 performing operations, 54 piecewised-defined functions and, 84 87, polynomials and, 301 quadratic equations and, raise to the power key, 57 range of a function and, rational functions and, nd key, 52, 53 sequences and, specific points and, square roots, 54, systems of nonlinear equations and, and systems of two-variable equations, table of values for sequences, 737 TRACE command, 64, 65 typing in a function, 63 WINDOW menu, window size and, 63, Xscl, 72 Yscl, 72 Y screen, 62 zeros/roots and, ZOOM Decimal, 65, 70 ZOOM Standard, 64, 70 Graph of an equation, defined, 514, 521 Graphs and graphing 78 combining functions and, , 157 composing functions and, concave down graphs, 137 concave up graphs, 137 of ellipses, 675, 678 exponential decay and, hole in graph, 354 of inverse functions, of linear equations with two variables, , 521 local maximums and minimums and, of logarithmic functions, of polynomials, 300, , solutions in three variables, Greatest common factor (GCF) factoring by, 20 21, 226 solutions to exponential equations and, Grouping, factoring by, 25 26, 226 Growth applications of, Horizontal asymptotes, defined, 349 Horizontal line, form of, 499 Horizontal line test, 188 Horizontal translations, 665 defined, 316 Hyperbolas as conic sections, 660, defined, 688 formulas for, 689 general form of, identifying, 699 reflective property of, 694 sketching, solutions, transforming hyperbola into standard form, vertical hyperbolas, I, defined, Identity, 43, 46 Identity matrices, 573 Imaginary numbers, Impossible events, 777 Inconsistent systems of equations, 515, 623 Increasing functions, , 138 Independent events, defined, 778 Independent systems of equations, 515 Independent variables defined, 107 functions and, 108, 109 Index defined, 4 of summation, Inequalities absolute value inequalities, linear inequalities, , A-1 A-3 polynomial inequalities, rational inequalities, reversing of, 262 solutions, systems of linear inequalities, A-4 A-6 Infinite sequences, 732, 751 Infinite series defined, 751 value for, 752 Infinite solutions, 46, 519, , 712 Infinite sums, 758 Inputs, , 123 Integers, Interval notation, 127 Inverse of exponential functions, formula for, 598 Inverse functions 202 defined, difficult inverses, 197 example of, finding inverse logically, , 398 finding inverse of one-to-one function, 192 finding inverses of non-one-toone functions, graphs of, observations of, Inverse matrix method, 603, , 633 Inverse method, systems of equations, Inverse properties of logarithms, 408 Inverse relations, 191 Inverse variation, A-15 A-16 defined, A-15 Irrational Conjugate Zeros Theorem, 338 Iterations, 223 Julia Set, 222 Least common denominator (LCD) rational equations and, 251 rational expressions and, 34 Least squares best fit, 530 Like terms, defined, 7 Limits, 349 Linear asymptotes, 353 Linear equations 51, solutions, 41 46,

4 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-4 I-4 Index Linear equations (continued) systems of two-variable equations, Linear function models, 532, 533, 537, 546, 549 Linear functions arithmetic sequences and, 739 common differences and, 293, 294 formulas of lines and, parallel and perpendicular lines and, range and, 125 slope formula and, as type of polynomial function, 288, Linear inequalities defined, A-1 solutions, , A-1 A-3 Linear models, data analysis, Linear polynomials, 288, , 293, 294, 302, 304 Linear programming, optimization, A-7 A-11 Lines formulas of, parallel and perpendicular lines, slope formula, Line solution, 613 Local maximums, 8, 139 Local minimums, 9 Logarithmic equations solutions, Logarithmic function models, 532 Logarithmic functions basics of, , 521 finding, , 524 properties of logarithms and, Logarithms applications of, defined, 399 estimating, evaluating, 400 exponents and, properties of, , 419 Logistics function models, 550 Log of 1 property of logarithms, Long division of polynomials, , 326, 617 Major axis, of ellipses, 673 Mandelbrot Set, 221 Mathematical induction, 754 Matrices addition of, additive identity for, 573 additive inverse for, applications of, , basics of, , defined, 568 determinants and, Gaussian elimination, , 633 identities and inverses, inverse matrix method, 603, , 633 matrix multiplication, matrix operations, multiplicative identity for, multiplicative inverses for, scalar multiplication and, subtraction of, systems of equations and, word problems and, Matrix equations Cramer s Rule, defined, 603 graphic representations of solutions in three variables, inverse method, solutions, Minor, 597 Minor axis, of ellipses, 673 Monomials division of monomial by monomial, 15 Multiplication of complex numbers, defined, 2 factoring as undoing of, 20 of functions, 151 of matrices, of polynomials, 14 of radical expressions, 8 of rational expressions, scalar multiplication, Multiplicative identity, 187 Multiplicative identity for matrices, Multiplicative inverse, 187 Multiplicative inverses for matrices, Multiplicity, 229, 308 Mutually exclusive events, defined, 779 Natural logarithms, 407 Natural log function models, , 537, 547 Negative rule for exponents, 2, 3 Non-quadratic functions, translations of, No real roots, 234 No solution, 45, 48, 515, 518, 612, 712, nth Partial Sum defined, 751, 752 finding, Objective function, A-7 Oblique asymptotes, defined, 352 Odd functions, Odd-power polynomials, One solution, 45, 515, 612, 712 One-to-one functions, , Optimization, linear programming, A-7 A-11 Order of combinations, 766 of matrices, 568 of permutations, Ordered pairs, Order of operations, graphing calculators, 52, 55 Outcomes, defined, 776 Outputs, , 123 Parabolas combinations of translations, , compression and stretching, , 666 as conic sections, 660, defined, 661 formulas for, , 665 general form of, 705 horizontal translations of, 316, 665 identifying, 699 multiplication by negative, quadratic polynomials and, 314, 661 sideways parabolas, , 669 sketching and labeling, solutions, in standard position, transforming parabola into standard form, vertical translations of, , 665 Parallel lines defined, 501 finding, Partial sums, series, 751, 752, Perfect square trinomials, Permutations counting theory and, defined, Permutations formula, defined, 764 Perpendicular lines defined, 502 finding, PH Formula, Piecewised-defined functions, graphing calculators, 84 87, Plane solution, 613 Point of symmetry (center) defined, 672 of ellipses, Point-slope form of a line, 498 Polynomial functions, 225 Polynomial inequalities, solutions, Polynomials addition of, 13 characteristics of, constant polynomials, , 294, 302 continuity and, 300, 301 cubic polynomials, 302, 304 defined, 12 division of, 15 17, , 617 end behavior and, factoring, fifth-power polynomials, 302 finding polynomial through three points, introduction to, linear polynomials, 288, , 293, 294, 302, 304 long division and, , 326, 617 multiplication of, 14 operations on, quadratic polynomials, 288, , 293, 294, 302, 304, 314, quartic polynomials, 302, 304 rational functions and, remainder theorem, shapes of polynomial graphs, simplification of, 13, 14 sketching by hand, 307 subtraction of, 13 symmetry and, translating functions and, x-intercepts and, zeros/roots of, Power function models, 548 Power property of logarithms, Power rule for exponents, 2, 3 Power Rule for Logarithms, 416 Principal square root, 5, Probability basics of, defined, 776 use of complement, Product property for logarithms, Product rule for exponents, 2, 3 Product Rule for Logarithms, 415 Product rule for radicals, 6

5 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-5 Index I-5 Pythagorean Theorem defined, 660 distance formula and, Quadratic asymptotes, 355 Quadratic equations completing the square, factoring method, quadratic formula, recognition of quadratics, square root method, Quadratic formula defined, 232 solving quadratic equations and, solving quadratic-like equations and, Quadratic function models, 532, , 537, 546, 549, 551, 552 Quadratic inequalities, solutions, Quadratic-like equations, solutions, Quadratic polynomials end behavior and, 304 finding through three points, parabola as, 314, 661 shape characteristics, 302 translating functions and, 314 as type of polynomial function, 288, , 293, 294 Quadratic trinomials, factoring, 21 Quartic function models, 547, 548, 552 Quartic polynomials, 302, 304 Quotient property of logarithms, Quotient rule for exponents, 2, 3 Quotient Rule for Logarithms, 416 Quotient rule for radicals, 6 Quotients, defined, 16 Radical expressions addition of, 7 multiplication of, 8 simplification of, 6 subtraction of, 7 Radicals defined, 4 fractional exponents and, 6 operations on, 7 8 rationalizing denominators and, 8 9 Radicands, defined, 4 Range of a function, 122, , 193 of combined functions, of composed functions, defined, 120 of square roots, 123, Rate of change, , 291, 292, 294 Rational equations, solutions, Rational expressions addition of, defined, 31 division of, 33 multiplication of, operations on, simplification of, 31 subtraction of, Rational functions examples of, horizontal asymptotes and, oblique asymptotes and, vertical asymptotes and, x-intercepts for, 356 Rational inequalities, solutions, Rationalizing denominators, 6, 8 9 Rational Zeros Theorem, defined, 336 Real-value inputs, 123, 152 Real-value outputs, 123 Recursive sequences, defined, 737 Reduced row echelon form of matrix, 593 Reflective property of ellipses, 679 of hyperbolas, 694 of parabolas, 663 Regression analysis, 530 Relations defined, 100, 102, 120 functions and, , , 665 inverse relations, 191 Relative maximums, of functions, Relative minimums, of functions, Remainder Theorem, defined, 329 Restricted domain, 123, 124, Roots. See Zeros/roots Roots of a polynomial, defined, 335 Rotated conics, 701 Rotation translation, 665, 666 defined, 317 Sample spaces, defined, 776 Scalar multiplication, matrices, Scientific notation, 3 4 defined, 3 Self-similar, fractals as, 222 Sequence of partial sums defined, 751 series, Sequences arithmetic sequences, basics of, defined, 732, 752 finding nth term of, geometric sequences, recursive sequences, series and, Series basics of, defined, 751, 752 partial sums, summation notation and, Sierpinski s Triangle, 222 Simplification of complex fractions, of complex numbers, 218 of factorials, 767 of fractional exponents, 5 of polynomials, 13, 14 of radical expressions, 6 of rational expressions, 31 of square roots, , 218 Sine function, Singular matrix, 596 Slope formula, , , Slope-intercept form of a line, Smooth polynomials, 300, 301 Solutions absolute value equations, absolute value inequalities, composed functions and realvalued solutions, 159 counting principle, 762 equations, exponential equations and, extraneous solutions, 242 flow charts for solving equations, fractional exponent equations, functions for dependent variables, inequalities, linear equations, 41 46, linear inequalities, , A-1 A-3 logarithmic equations and, parabolas, polynomial inequalities, quadratic equations, quadratic-like equations, rational equations, rational inequalities, sequences, , square root equations, , 248 systems of equations and, systems of linear inequalities, A-4 A-6 systems of nonlinear equations, Special binomials, 24 25, 226 Square matrices, 592, 595, 598 Square root method, Square roots absolute value equations and, domain and range and, 123, graphing calculators, 54, imaginary numbers and, principal square root, 5, simplification of, , 218 solutions of square root equations, , 248 Standard Form of a Circle, defined, 679 Standard form of a line, Standard Form of an Ellipse, defined, 676 Standard Form of an Hyperbola, defined, 693 Standard Form of a Non-Function (Sideways) Parabola, defined, 669 Standard Form of the Parabola Function, defined, 668 Standard position ellipses, 674, 700 hyperbolas, 689 parabolas, 662, Stretching, , 666 defined, 318 Substitution method systems of equations, , 521 systems of nonlinear equations, 711, 713 Subtraction of complex numbers, of functions, 151, 157 of matrices, of polynomials, 13 of radical expressions, 7 of rational expressions, Summation notation defined, 752 series, Sum of an Infinite Geometric Series, defined, 758

6 5639_Holtfrerich_Index 6/2/05 11:45 AM Page I-6 I-6 Index Sum of two cubes formula, 24 Symmetry axis of, 662 polynomials, Synthetic division of polynomials, , 617 Systems of equations addition method, , 521, , 621 applications with matrices, Cramer s Rule, defined, 514 exponential and logarithmic equations, Gaussian elimination and, graphical solutions, , 521 inverse method, matrices and, substitution method, , 521 translating word problems and, two-variable equations, , 712 Systems of linear inequalities, solutions, A-4 A-6 Systems of logarithmic equations, Systems of nonlinear equations, solutions, Tables combining functions and, 155, 157 common differences and, 291, , , 382, 383, 384 common ratios and, 381, 382, 383, 384 composing functions and, , 163 compound interest and, exponential characteristics and, 393 exponential decay and, , exponential growth and, increasing and decreasing functions and, 138 local maximums and minimums, of logarithmic functions, 404, 406 number e and, 397 table of values for sequences, 737 Terms of arithmetic sequences, defined, 7 of recursive sequences, of sequences, , Test Point Method, , TI-83/84 absolute value, Gaussian elimination method and, , inverse of matrix and, MATH menu, 58 matrices and, minus sign key, modeling with, , , 550 negative sign key, piecewise-defined functions and, QUIT command, 54 relative maximums and relative minimums, sequences and, TRACE command, 64, 65, 73 window size and, Yscl, 72 zeros/roots and, ZOOM Decimal, 65, 75 ZOOM OUT, 71 ZOOM Standard, 64, 70, 73 TI-86 absolute value, EXIT key, 54 Gaussian elimination method and, , inverse of matrix and, MATH menu, 58 matrices and, minus sign key, modeling with, , , 550 negative sign key, piecewise-defined functions and, relative maximums and relative minimums, sequences and, TRACE command, 64, 65, 73 window size and, Yscl, 72 zeros/roots and, ZOOM Decimal, 65, 66, 75 ZOOM OUT, 71 ZOOM Standard, 64, 70, 73 Translated conics, 700 Transverse axis, of hyperbolas, 689 Trinomials completing the square and, 701 factoring, 21 23, 226 multiplying binomial by trinomial, 14 Unknown constants, 521 Variable matrix, 603 Variables defined, 107 in denominators, dependent variables, 107, 108, 109, graphic representations of solutions in three variables, independent variables, 107, 108, 109 systems of two-variable equations, , 712 Variation direct variation, A-14 A-15 inverse variation, A-15 A-16 other variation statements, A- 17 Velocity, 292 Vertical asymptotes, defined, 348 Vertical line, form of, 499 Vertical line test, 106, 188, 676 Vertical translations, , 665 defined, 315 Vertices of ellipses, 673 of hyperbolas, 689 of parabolas, 661, 664, 665, 667 of quadratic polynomials, 314 Word problems matrices and, systems of equations and, x-intercepts 395 polynomials and, for rational functions, 356 x-intercept Theorem, y-intercepts, exponential functions, 395 Zero of a polynomial, defined, 335 Zero rule, 2 Zeros/roots polynomials and, roots of polynomials, , , zeros of polynomials, , Zeros Theorem, defined, 339