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5-1 Study Guide - Operations with Polynomials 12-4+6. = C. 19. 2 x-2y. 4. yoy. Y to b x4y-1 as. 7.(-5a²b³)² (abc)2. 2. {(25a4b" Xa²b²²).
Chapter 9 Resource Masters
Study Guide and Intervention Workbook 6. All quadratic equations have two real solutions. 7. ... Approximate the zeros of this function by graphing.
Chapter 7: Polynomial Functions
roots of a polynomial function and then find those roots. Study Guide and Intervention CRM pp. ... Lessons 7-4
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Study Guide and Intervention The zeros of a quadratic function are the x-intercepts of its graph. ... Graph the related function f(x) = x²+x-6.
Study Guide and Intervention Workbook
1 2 3 4 5 6 7 8 9 10 047 14 13 12 11 10 09 08 organized by chapter and lesson with two Study Guide and Intervention ... the zero of this function.
Chapter 7 Resource Masters
Study Guide and Intervention Workbook 1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02 ... exactly n roots in the set of complex numbers.
Public Assistance Program and Policy Guide Version 4
06/01/2020 Study Requirements for Drainage Structures and Culverts. March 15 2019
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4-1 Study Guide and Intervention f(1)=3(1)² — 6(1) + 7 = 4 so the minimum value ... or the zero(s) of the related quadratic function. 2 4 6 X.
Study Guide and Intervention Workbook
1 2 3 4 5 6 7 8 9 10 045 14 13 12 11 10 09 08 organized by chapter and lesson with two Study Guide and Intervention ... 6-7 Roots and Zeros .
9-4 Study Guide and Intervention - Solving Quadratic Equations by
9-4 Study Guide and Intervention Solve Quadratic Equations Using the Square Root Property You may be able to use the Square Root ... + 6(1) = 7 and (–7).
Roots and Zeros - Weebly
DATE PERIOD 5-7 Study Guide and Intervention Roots and Zeros Synthetic Types of Roots The following statements are equivalent for any polynomial function f (x) c is a zero of the polynomial function f(x) c is a root or solution of the polynomial equation f(x) = 0 (x - c) is a factor of the polynomial f(x)
6-7 Study Guide and Intervention - Weebly
4 + 7x = ?7x - 9 10 4 3 ? 2x + 11 - 2 = 10 11 2 ?x - 11 = ?x + 4 12 (9x - 11) ?1 2 = x + 1 Solve Radical Equations The following steps are used in solving equations that have variables in the radicand Some algebraic procedures may be needed before you use these steps Study Guide and Intervention
Chapter 6 Resource Masters - KTL MATH CLASSES
Study Guide and Intervention Each lesson in Algebra 2addresses two objectives There is one Study Guide and Intervention master for each objective WHEN TO USE Use these masters as reteaching activities for students who need additional reinforcement These pages can also be used in conjunction with the Student Edition as an instructional tool
5-7 Study Guide and Intervention - Ms Brown
2 imaginary zeros Solve each equation State the number and type of roots 1 x2 + 4x - 21= 0 2 2x3 - 50x = 0 3 12x3 + 100x = 0 State the possible number of positive real zeros negative real zeros and imaginary zeros for each function 4 f(x) = 3x3 + x2 - 8x - 12 5 f(x) = 3x5 - x4 - x3 + 6x2 - 5 Example 1 Example 2 Exercises 5-7
Searches related to 6 7 study guide and intervention roots and zeros
Step 1 If the index of the root is even identify the values of the variable for which the radicand is nonnegative Step 2 Solve the inequality algebraically Step 3 Test values to check your solution Example: Solve 5 –? ????+ ?? –3 Since the radicand of a square root must be greater than or equal to zero first solve 20x + 4 ? 0
Chapter 7
Resource Masters
Consumable Workbooks
Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Study Guide and Intervention Workbook0-07-828029-XSkills Practice Workbook0-07-828023-0
Practice Workbook0-07-828024-9
ANSWERS FOR WORKBOOKSThe answers for Chapter 7 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teacher, and families without charge; and be used solely in conjunction with GlencoeÕs Algebra 2.Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.Send all inquiries to:
The McGraw-Hill Companies
8787 Orion Place
Columbus, OH 43240-4027
ISBN: 0-07-828010-9Algebra 2
Chapter 7 Resource Masters
1 2 3 4 5 6 7 8 9 10 066 11 10 09 08 07 06 05 04 03 02
Glencoe/McGraw-Hill
Study Guide and Intervention
Polynomial Functions
NAME ______________________________________________ DATE ____________ PERIOD _____7-17-1
©Glencoe/McGraw-Hill375Glencoe Algebra 2
Lesson 7-1
Polynomial Functions
Apolynomial of degree nin one variable xis an expression of the formPolynomial ina0
x n a 1 x n1É a
n2 x 2 a n1 xa nOne Variable
where the coefficients a 0 , a 1 , a 2 , É, a n represent real numbers, a 0 is not zero, and nrepresents a nonnegative integer. The degree of a polynomialin one variable is the greatest exponent of its variable. The leading coefficientis the coefficient of the term with the highest degree. Apolynomial function of degree ncan be described by an equation of the formPolynomialP(x) a0
x n a 1 x n1É a
n2 x 2 a n1 xa nFunction
where the coefficients a 0 , a 1 , a 2 , É, a n represent real numbers, a 0 is not zero, and nrepresents a nonnegative integer.What are the degree and leading coefficient of 3x
2 2x 4 7 x 3 Rewrite the expression so the powers of xare in decreasing order. 2x 4 x 3 3x 2 7 This is a polynomial in one variable. The degree is 4, and the leading coefficient is 2.Find f(5) if f(x) x3
2x 210x20.
f(x) x 3 2x 210x20Original function
f(5) (5) 3 2(5) 210(5) 20Replace xwith 5.
125 50 50 20Evaluate.
5Simplify.
Find g(a
21) if g(x) x
2 3x4. g(x) x 23x4Original function
g(a 2 1) (a 2 1) 2 3(a 21) 4Replace xwith a
2 1. a 4 2a 2 1 3a 23 4Evaluate.
a 4 a 26Simplify.
State the degree and leading coefficient of each polynomial in one variable. If it is not a polynomial in one variable, explain why.8; 8 1.3x 4 6x 3 x 2124; 32.100 5x
3 10x 77; 103.4x
6 6x 4 8x 8 10x 2 20 4.4x 23xy16y
2 5.8x 3 9x 5 4x 2 366.not a polynomial in 5; 9one variable; contains 6; two variables
Find f(2) and f(5) for each function.
7.f(x) x2
98.f(x) 4x
3 3x 22x19.f(x) 9x
3 4x 2 5x75; 16 23; 586 73; 1243
1 1 72x3 36x
6 25x
2
18Example1Example1
Example2Example2
Example3Example3
ExercisesExercises
Chapter 7 Test, Form 1
NAME DATE PERIOD
SCORE©Glencoe/McGraw-Hill429Glencoe Algebra 2
Assessment
Write the letter for the correct answer in the blank at the right of each question.1.Find p(3) if p(x)4x.
A.12B.4C.1D.71.
2.State the number of real zeros for the function
whose graph is shown at the right.A.0B.1
C.2D.32.
For Questions 3 and 4, use the graph shown at the right.3.Determine the values of xbetween which a real zero
is located.A.between 1 and 0
B.between 6 and 7
C.between 2 and 1
D.between 2 and 33.
4.Estimate the x-coordinate at which a relative minimum occurs.
A.3B.2C.0D.14.
5.Write the expression x4
5x 28 in quadratic form, if possible.
A.(x 2 2 5(x 2 )8B.(x 4 25(x4 )8 C.(x 2 2 5(x 2 )8D.not possible5.
6.Solve x
4 13x 2 360.A.3,2, 2, 3B.9,4, 4, 9C.2, 3, 2i,3iD.2,3, 2i,3i6.
7.Use synthetic substitution to find f(3) for f(x)x
29x5.A.23B.16C.13D.417.
8.One factor of x
3 4x 211x30 is x2. Find the remaining factors.
A.x5,x3B.x3,x5C.x6,x5D.x5,x6 8.
9.Which describes the number and type of roots of the equation 4x70?
A.1 imaginary rootB.1 real root and 1 imaginary rootC.2 real rootsD.1 real root9.
10.Which is nota root of the equation x3
x 210x8 0?
A.1B.4C.2D.110.
11.List all of the possible rational zeros of f(x)x
3 7x 2 8x6. A.1, 1 2 1 3 1 6B.0,1,2,3,6
C.1,2,3,4,6D.1,2,3,611.77
xO f (x)xO f(x)Standardized Test Practice
Student Record Sheet(Use with pages 406-407 of the Student Edition.) ©Glencoe/McGraw-HillA1Glencoe Algebra 2NAME DATE PERIOD 77Answers
Select the best answer from the choices given and fill in the corresponding oval. 1471025811
36912
Solve the problem and write your answer in the blank. Also enter your answer by writing each number or symbol in a box. Then fill in the corresponding oval for that number or symbol.
13 15 17 19
14 16 18
Select the best answer from the choices given and fill in the corresponding oval.20 22 24
21 23DCBADCBA
DCBADCBADCBA
0009999876543
2 1 876543
2 18765
43
2 18765
43
2quotesdbs_dbs12.pdfusesText_18
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