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
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
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 = -11+ 4z 2 + 5z - 6z 3 2 Teacher Notes Order of Powers 3
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
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 2 + 12 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
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
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 3 + 24x + 2 click 3rd for example degree Degree 7
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
HINT Practice: Tell whether each expression is a polynomial or not. Why? Next 1 5x 3-4x + 1 2 3x 3 3 x 4 x + 3 Click here for the answer Practice 1 9
HINT Practice: Write the coefficients of the polynomials under each polynomial Next 1 5x 4-7x 3 + x 2 - x + 8 2-3x 5 + 4x 3 - x 2-12 Click here for the answer Practice 2 10
HINT Practice: Name the Polynomials 1 13x - 7 5x 3 4 HINT 2 6x 2 + 11x - 8 5 5x 4 + x 7 3 x 3 + x 2 + x +1 6 6x 2-2x 2 + 4x - 5 Click here for the answer Practice 3 11
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
Practice: Write the coefficients of the polynomials under each polynomial HINT Back 1 5x 4-7x 3 + x 2 - x + 8 5 7 1 1 8 ; ; ; ; 2-3x 5 + 4x 3 - x 2-12 3; 4; 1; 12 Answers 2 13
HINT Practice: Name the Polynomials Back Next 1 2 13x - 7 5x 3 linear binomial cubic monomial 6x 2 + 11x - 8 5 5x 4 + x 7 quadratic trinomial 7th degree binomial 4 HINT 3 x 3 + x 2 + x +1 6 6x 2-2x 2 + 4x - 5 cubic polynomial w/4 terms quadratic trinomial Answers 3 14
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
2 Yes No Is x 5 y 4 z 2 a polynomial? Yes or No Dec 13 3:02 AM 16
3 True False x 3 y 7x + 2z is a monomial. True or False Dec 13 3:02 AM 17
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
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
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
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
8 14x 2 y 3 /10x 4 y = 7y 2 /5x 2 True False True or False Dec 13 3:02 AM 22
9 Simplify this expression. ( 3x 2 + 4x)(10x 2 + 10x) Multiple choice A 30x 4 + 10x 3 40x 2 B 30x 4 10x 3 40x 2 C 30x 4 + 10x 3 + 40x 2 D 30x 4 + 10x 3 + 40x 2 Dec 13 3:02 AM 23
Simplify this expression. ( 3x 2 + 4x)(10x 2 + 10x) Mar 10 9:38 AM 24
10 Simplify this expression. (25x 4 10x 3 + 32x 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
Attachments Naming Polynomials.pdf