8.1 Degree, Standard Form 2017 Ink.Notebook February 08, 2018

8.1 degree, standard form 2017 ink.notebook February 08, 2018

Page 59 page 59 Page 60

8.1 Polynomials ‐ Degree and Standard Form

Lesson Objectives Standards Lesson Notes

8.1 Polynomials A.SSE.1 I will find the degree of a polynomial A.SSE.1 I will identify the leading coefficient of a polynomial A.SSE.2 I will rewrite a polynomial into standard form

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1 8.1 degree, standard form 2017 ink.notebook February 08, 2018

My Definition: Characteristics: Lesson Objectives Standards Lesson Notes An expression that EXCEPTIONS: can have constants, No division by a variable variables, and exponents Only whole number exponents A.SSE.1 Interpret expressions that Named by degree and Can't have an infinite represent a quantity in terms of its context. number of terms number of terms Polynomial Example: Counterexample: a) Interpret parts of an expression, such as 4 terms, factors, and coefficients. x + y = 5 has equal sign 6 2 -2 5x + 4x - 1 x + y has negative exponent 5xy2 - 3x + 5y3 - 3 2 x has a variable on bottom Press the tabs to view details.

Polynomials can be named by the number of terms

Terms Name Example

2 8.1 degree, standard form 2017 ink.notebook February 08, 2018

Let's Practice. Name the following polynomials. 1. –7 + 3n3 2. 2x2 3x4 + 5x + 6 binomial polynomial 3. 5 4. 2x + 3y monomial binomial 5.5x3 + 4x2 - x + 1 6. 2x2 + 5x + 6 polynomial trinomial 7.-x4 + 3x2 - 11 8. 2x3y4 trinomial monomial

9. 10. 6x2 + 3y–1

monomial binomial trinomial polynomial

Degree of a polynomial. The highest exponent or the sum of the exponents in a monomial.

11. 2x3y4 monomial add the exponents

12.2x4 + 3y8 NOT a monomial take the highest exponent

13. 2x2 + 5x2y3 + 6xy5 add the exponents in each individual monomial and then find the highest

14.5x 15. 2

3 8.1 degree, standard form 2017 ink.notebook February 08, 2018

Find the degree of each polynomial. 16. 4x2y3z 17. –2abc

18. x4 − 6x2 − 2x3 − 10 19. 18x2 + 4yz − 10y

20. 22 21. 15m

22. −2r8x4 + 7r2x − 4r7x6 23. 2x3y2 − 4xy3

Standard Form The terms of a polynomial are arranged so that the terms are in order from greatest degree to least degree. Leading Coefficient The number in front of the first term when the polynomial is in standard form. Example: -x5 + 8x4 - x2 - 15 (highest exponent is the first term) Leading Coefficient: -1 Write each polynomial in standard form. Identify the leading coefficient. 24. 5x + 6 + 2x2 25. − x2 − 2 + 5x4 + 3x

26. 5x + x2 + 6 27. 6x + 9 − 4x2

28. x4 + x3 + x2 29. 2x3 − x + 3x7

4 8.1 degree, standard form 2017 ink.notebook February 08, 2018

On Your

On the Worksheet Whiteboards

Determine whether each expression is a polynomial. If so, Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial. Then find the degree of the polynomial. identify the polynomial as a monomial, binomial, or trinomial. Monomial, Degree of Polynomial Expression Binomial,or the ? 36a) b) Trinomial? Polynomial 1. 3x 7xyz 2. 25 Monomial Monomial 3. 7n3 + 3n4 Binomial polynomial Binomial polynomial 4. 9x3 + 4x + x + 4 + 2x Monomial = 1 piece Trinomial Trinomial

Binomial = 2 pieces Degree :

Trinomial = 3 pieces

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2 Find the degree of each polynomial. 7x − x + 5c) d) 8g h − 7gh + 2 (The highest exponent or the sum of the exponents in a monomial.) e) 9x2 + yz8 f) 8b + bc5 Monomial Monomial

Binomial polynomial Binomial polynomial

Trinomial Trinomial g) h3m + 6h4m2 − 7

Write each polynomial in standard form. Identify the leading coefficient.

xh) 4 + 4x3 − 7x5 + 1 3xi) 6 − x5 + 2x8 On the

2xj) 7 − x8 k) 3x + 5x4 − 2 − x2 Worksheet

6 8.1 degree, standard form 2017 ink.notebook February 08, 2018

To complete each sentence, write a letter from the column at the right.

a. monomial _____1. 7 – 3x2 is a(n) __?__. b. binomial c. trinomial _____2. The degree of the polynomial d. 0 6x2 – 2x + 1 is __?__. e. 1 f. 2 _____3. In 7x3 – 2x – 1, 1 is a(n) __?__. g. 3 h. constant i. exponent _____4. In 4x2 – 3x + 1, 2 is a(n) __?__. j. variable Homework k. degree _____5. The degree of the monomial 1 is __?__.

_____6. 9y2 – 2y + 3 is a(n) __?__.

To complete each sentence, write a letter from the column at the right. Determine whether each expression is a _____7. In the polynomial 3c3 – 2c + 1, a. monomial polynomial. If so, identify the polynomial c is the only __?__. b. binomial as a monomial, binomial, or trinomial. c. trinomial d. 0 _____8. – 7x3y4 is a(n) __?__. 2 e. 1 12. 7ab + 6b – 2a3 13. 3x2 f. 2 _____9. The degree of the polynomial g. 3 7 – 4x is __?__. h. constant i. exponent _____10. The __?__ of a monomial is j. variable the sum of the exponents of k. degree all of its variables. 15. 5m2p3 + 6 _____11. The degree of the polynomial 7x3 + 2x2 – 7x is __?__.

7 8.1 degree, standard form 2017 ink.notebook February 08, 2018

Determine whether each expression is a Find the degree of each polynomial. polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial. 18. −3 19. 6p3 – p4

16. 2y – 5 + 3y2 17. 5q−4 + 6q

20. −7z 21. 4h2j3 – h3k3

Find the degree of each polynomial. Find the degree of each polynomial.

2 4 2 5 22. 2a2b5 + 5 – ab 23. 12 – 7q2t + 8r 26. 4x − 1 27. 4x y − 8zx + 2x

24. 3.5 25. 6df3 + 3d2f2 28. 9abc + bc − n5 29. 5x4 − 12x − 3x6

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Write each polynomial in standard form. Identify the leading coefficient.

Write each polynomial in standard form. Identify the leading coefficient. 34. 2x5 – 12 + 3x 35. –y3 + 3y – 3y2 + 2 30. −4x2 + 9x4 − 2x 31. 2x + x2 − 5

36. 4z – 2z2 – 5z4 37. 2a + 4a3 – 5a2 – 1

32. 20x − 10x2 + 5x3 33. x3 + x5 − x2

Write each polynomial in standard form. Identify the leading coefficient.

38. 11t + 2t2 – 3 + t5 39. 2 + r – r3 42. You have a coupon from The Really Quick Lube Shop for an $8 off oil change this month. An oil change costs $19.95, and a new oil filter costs $4.95. You use the coupon for an oil change and filter. Before adding tax, how much should you pay?

a) $11.95 b) $16.90

c) $24.90 d) $27.95

9 8.1 degree, standard form 2017 ink.notebook February 08, 2018

Solve each by writing your answer as a FRACTION or a WHOLE number.

43. Create a trinomial with a degree of 2, whose leading –4 – –3 coefficient is –8 44. 4 45. (15)

46. 47. 13.40

Answers: Solve each by writing your answer as a FRACTION or a WHOLE number. 1) B 3) H 5) D 7) J 9) E 11) G 13) monomial

15) binomial 17) not a poly 19) 4 21) 6 23) 3 25) 4 – 2 48. ( 5) 49. 27) 5 29) 6 31) x2 + 2x – 5, LC = 1 33) x5 + x3 – x2, LC = 1

35) –y3 – 2y2 + 3y + 2, LC = –1 37) 4a3 – 5a2 + 2a – 1, LC = 4

39) –r3 + r + 2, LC = –1 41) –b6 – 9b2 + 10b, LC = –1

43) WILL VARY: –8x2 + 2x+ 1

45) 47) 1 49)