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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 Unit 8 Polynomials 8.1 Polynomials ‐ Degree and Standard Form Lesson Objectives Standards Lesson Notes 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 Press the tabs to view details. Press the tabs to view details. 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 5 8.1 degree, standard form 2017 ink.notebook February 08, 2018 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 8 8.1 degree, standard form 2017 ink.notebook February 08, 2018 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) 10.
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