Polynomials. Title Page. Prior Knowledge: understanding of coefficients and terms
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1 Polynomials Title Page Subject: Polynomials Topic: Classifying Polynomials by Degree and Number of Terms. Also a review of Coefficients. Grade(s): 8th 10th grade Prior Knowledge: understanding of coefficients and terms Lesson objectives Teachers' notes Lesson notes Title Page 1
2 Polynomials Lesson Objectives To know definition of specialized names polynomials, ie, monomial, binomial, trinomial, polynomial. Be able to determine degree of a given polynomial. To classify any polynomial by degree and number of terms. To identify any coefficient of a given term of a polynomial. Lesson objectives Teachers' notes Lesson notes Lesson Objectives 2
3 Polynomials Objective: to learn to write polynomials in ascending order and descending order of powers Write Polynomial in ascending order of powers. = 5z - 6z 3 + 4z 2-11 = z 2 + 5z - 6z 3 2 Teacher Notes Order of Powers 3
4 Polynomials Objective: to learn to write polynomials in ascending order and descending order of powers Write Polynomial in descending order of powers. = 8x 4-11x + 2x 5 - x 2 Teacher Notes = 2x 5 + 8x 4 - x 2-11x 2 Order of Powers 4
5 Pull an expression that has only +,, or by or of the variables Polynomials Polynomial: Stop Objective: to identify polynomials Teacher Notes Polynomials Ex. 1 3 there is only mult. by or of the variable Ex. 2 Click to reveal reason why. 3x Click to reveal reason why. there is only mult. by or of the variable Ex. 3 6x there is only add. and mult. by or of the variable Click to reveal reason why. Pull Stop Pull Stop Pull Stop Stop Pull Stop Pull Ex. 1 Not Polynomials 5 x Click to division reveal by a reason variablewhy. Ex. 2 x + 5 Click to reveal absolute reason value why. Polynomials 5
6 Pull Polynomials Monomial: Stop Objective: to name polynomials by number of terms Teacher Notes Monomials Binomials Trinomials 3ab 13x 4 9x 2 2x + 11 Teacher Notes Pull Pull 1 2 Bi Tri 3 Mono means... means... Pull means... Terms 6
7 Polynomials Degree: exponent of highest power Stop Pull Objective: to name polynomials by degree Teacher Notes Linear: 1st degree polynomial 7x 4 click 1st for example degree Quadratic: 2nd degree polynomial 3x 2 4x + 6 click 2nd for example degree Cubic: 3rd degree polynomial x x + 2 click 3rd for example degree Degree 7
8 Polynomials Ex. 3 7x 3 1st 3rd 2nd Objective: to name polynomials by degree and number of terms Polynomials Degree Degree Name Polynomial Name Ex. 1 17x 2 + 6x 4 Ex. 2 5x 7 2nd 1st quadratic linear trinomial binomial 3rd cubic monomial linear cubic monomial trinomial quadratic quadratic binomial Teacher Notes Pull Stop Pull Stop Stop Pull Teacher Notes Naming Polynomials 8
9 HINT Practice: Tell whether each expression is a polynomial or not. Why? Next 1 5x 3-4x x 3 3 x 4 x + 3 Click here for the answer Practice 1 9
10 HINT Practice: Write the coefficients of the polynomials under each polynomial Next 1 5x 4-7x 3 + x 2 - x x 5 + 4x 3 - x 2-12 Click here for the answer Practice 2 10
11 HINT Practice: Name the Polynomials 1 13x - 7 5x 3 4 HINT 2 6x x x 4 + x 7 3 x 3 + x 2 + x x 2-2x 2 + 4x - 5 Click here for the answer Practice 3 11
12 Practice: Tell whether each expression is a polynomial or not. Why? HINT Back 1 5x 3-4x + 1 yes, only +,, by/of the variable 2 3x yes, only +,, by/of the variable 3 3 x 4 x + 3 no, by a variable no, absolute value Answers 1 12
13 Practice: Write the coefficients of the polynomials under each polynomial HINT Back 1 5x 4-7x 3 + x 2 - x ; ; ; ; 2-3x 5 + 4x 3 - x ; 4; 1; 12 Answers 2 13
14 HINT Practice: Name the Polynomials Back Next x - 7 5x 3 linear binomial cubic monomial 6x x x 4 + x 7 quadratic trinomial 7th degree binomial 4 HINT 3 x 3 + x 2 + x x 2-2x 2 + 4x - 5 cubic polynomial w/4 terms quadratic trinomial Answers 3 14
15 1 True False An algebraic expression that has more than one term is called a polynomial. True or False Dec 13 3:02 AM 15
16 2 Yes No Is x 5 y 4 z 2 a polynomial? Yes or No Dec 13 3:02 AM 16
17 3 True False x 3 y 7x + 2z is a monomial. True or False Dec 13 3:02 AM 17
18 4 Simplify this expression. (2x + 4) ( x + 9) Multiple choice A 5 3x B x 5 C 5x 3 D 3x 5 Dec 13 3:02 AM 18
19 5 Simplify this expression. (4x 2-5x + 9) + (10x 2-7x - 1) Multiple choice A 14x 2 12x + 8 B 14x 2 2x + 8 C 14x 2 12x 8 D 12x 2 14x + 8 Dec 13 3:02 AM 19
20 6 True The expression (3x 5 y 6 )(5x 8 y 2 ) can be simplified to 15x 40 y 12. False True or False Dec 13 3:02 AM 20
21 7 Simplify this expression. x 4 /x Multiple choice A x B x 2 C x 3 D x 4 Dec 13 3:02 AM 21
22 8 14x 2 y 3 /10x 4 y = 7y 2 /5x 2 True False True or False Dec 13 3:02 AM 22
23 9 Simplify this expression. ( 3x 2 + 4x)(10x x) Multiple choice A 30x x 3 40x 2 B 30x 4 10x 3 40x 2 C 30x x x 2 D 30x x x 2 Dec 13 3:02 AM 23
24 Simplify this expression. ( 3x 2 + 4x)(10x x) Mar 10 9:38 AM 24
25 10 Simplify this expression. (25x 4 10x x 2 20x + 12) (5x 2 4x + 2) Multiple choice A 5x 2 + 2x + 6 B 5x 2 6x + 10 C 5x + 2x 6 D 5x 2 6x + 10 Dec 13 3:02 AM 25
26 Attachments Naming Polynomials.pdf
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Syllabus Objective: 9.1 The student will add, subtract, multiply, and factor polynomials connecting the arithmetic and algebraic processes. Teacher Note: A nice way to illustrate operations with polynomials
Course Number 420 Title Algebra I Honors Grade 9 # of Days 60
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
Sections 7.2, 7.3, 4.1
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X On record with the USOE.
Textbook Alignment to the Utah Core Algebra 1 Name of Company and Individual Conducting Alignment: Chris McHugh, McHugh Inc. A Credential Sheet has been completed on the above company/evaluator and is
x On record with the USOE.
Textbook Alignment to the Utah Core Algebra 1 This alignment has been completed using an Independent Alignment Vendor from the USOE approved list (www.schools.utah.gov/curr/imc/indvendor.html.) Yes N/A
Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring
Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis