1 / 45

Splash Screen

Splash Screen. Five-Minute Check (over Lesson 5–1) CCSS Then/Now New Vocabulary Example 1: Divide a Polynomial by a Monomial Example 2: Division Algorithm Example 3: Standardized Test Example: Divide Polynomials Key Concept: Synthetic Division Example 4: Synthetic Division

kcastle
Télécharger la présentation

Splash Screen

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Splash Screen

  2. Five-Minute Check (over Lesson 5–1) CCSS Then/Now New Vocabulary Example 1: Divide a Polynomial by a Monomial Example 2: Division Algorithm Example 3: Standardized Test Example: Divide Polynomials Key Concept: Synthetic Division Example 4: Synthetic Division Example 5: Divisor with First Coeffecient Other than 1 Lesson Menu

  3. Simplify b2 ● b5 ● b3. A.b5 B.b8 C.b10 D.b30 5-Minute Check 1

  4. Simplify b2 ● b5 ● b3. A.b5 B.b8 C.b10 D.b30 5-Minute Check 1

  5. A. B. C. D. 5-Minute Check 2

  6. A. B. C. D. 5-Minute Check 2

  7. Simplify (10a2 – 6ab + b2) – (5a2 – 2b2). A. 15a2 + 8ab + 3b2 B. 10a2 – 6ab – b2 C. 5a2 + 6ab – 3b2 D. 5a2 – 6ab + 3b2 5-Minute Check 3

  8. Simplify (10a2 – 6ab + b2) – (5a2 – 2b2). A. 15a2 + 8ab + 3b2 B. 10a2 – 6ab – b2 C. 5a2 + 6ab – 3b2 D. 5a2 – 6ab + 3b2 5-Minute Check 3

  9. Simplify 7w(2w2 + 8w – 5). A. 14w3 + 56w2 – 35w B. 14w2 + 15w – 35 C. 9w2 + 15w – 12 D. 2w2 + 15w – 5 5-Minute Check 4

  10. Simplify 7w(2w2 + 8w – 5). A. 14w3 + 56w2 – 35w B. 14w2 + 15w – 35 C. 9w2 + 15w – 12 D. 2w2 + 15w – 5 5-Minute Check 4

  11. State the degree of 6xy2 – 12x3y2 + y4 – 26. A. 11 B. 7 C. 5 D. 4 5-Minute Check 5

  12. State the degree of 6xy2 – 12x3y2 + y4 – 26. A. 11 B. 7 C. 5 D. 4 5-Minute Check 5

  13. Find the product of 3y(2y2 – 1)(y + 4). A. 18y5 + 72y4 – 9y3 – 36y2 B. 6y4 + 24y3 – 3y2 – 12y C. –18y3 – 3y2 + 12y D. 6y3 – 2y + 4 5-Minute Check 6

  14. Find the product of 3y(2y2 – 1)(y + 4). A. 18y5 + 72y4 – 9y3 – 36y2 B. 6y4 + 24y3 – 3y2 – 12y C. –18y3 – 3y2 + 12y D. 6y3 – 2y + 4 5-Minute Check 6

  15. Content Standards A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Mathematical Practices 6 Attend to precision. CCSS

  16. You divided monomials. • Divide polynomials using long division. • Divide polynomials using synthetic division. Then/Now

  17. synthetic division Vocabulary

  18. Divide a Polynomial by a Monomial Sum of quotients Divide. = a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1 Answer: Example 1

  19. Divide a Polynomial by a Monomial Sum of quotients Divide. = a – 3b2 + 2a2b3 a1 – 1 = a0 or 1 and b1 – 1 = b0 or 1 Answer:a – 3b2 + 2a2b3 Example 1

  20. A. 2x3y – 3x5y2 B. 1 + 2x3y – 3x5y2 C. 6x4y2 + 9x7y3 – 6x9y4 D. 1 + 2x7y3 – 3x9y4 Example 1

  21. A. 2x3y – 3x5y2 B. 1 + 2x3y – 3x5y2 C. 6x4y2 + 9x7y3 – 6x9y4 D. 1 + 2x7y3 – 3x9y4 Example 1

  22. x(x – 5) = x2 – 5x –2x – (–5x) = 3x 3(x – 5) = 3x – 15 Division Algorithm Use long division to find (x2 – 2x – 15) ÷ (x – 5). Answer: Example 2

  23. x(x – 5) = x2 – 5x –2x – (–5x) = 3x 3(x – 5) = 3x – 15 Division Algorithm Use long division to find (x2 – 2x – 15) ÷ (x – 5). Answer: The quotient is x + 3. The remainder is 0. Example 2

  24. Use long division to find (x2 + 5x + 6) ÷ (x + 3). A.x + 2 B.x + 3 C.x + 2x D.x + 8 Example 2

  25. Use long division to find (x2 + 5x + 6) ÷ (x + 3). A.x + 2 B.x + 3 C.x + 2x D.x + 8 Example 2

  26. Aa + 3 B C D Divide Polynomials Which expression is equal to (a2 – 5a + 3)(2 – a)–1? Example 3

  27. Rewrite 2 – a as –a + 2. –a(–a + 2) = a2 – 2a –5a – (–2a) = –3a 3(–a + 2) = –3a + 6 Subtract. 3 – 6 = –3 Divide Polynomials Read the Test Item Since the second factor has an exponent of –1, this is a division problem. Solve the Test Item Example 3

  28. . Therefore, Divide Polynomials The quotient is –a + 3 and the remainder is –3. Answer: Example 3

  29. . Therefore, Divide Polynomials The quotient is –a + 3 and the remainder is –3. Answer: The answer is D. Example 3

  30. A. B. C. D. Which expression is equal to (x2 – x – 7)(x – 3)–1? Example 3

  31. A. B. C. D. Which expression is equal to (x2 – x – 7)(x – 3)–1? Example 3

  32. Concept

  33. 1 –4 6 –4 1 Synthetic Division Use synthetic division to find (x3 – 4x2 + 6x – 4) ÷ (x – 2). Step 1Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown. x3 – 4x2 + 6x – 4  1 –4 6 –4 Step 2Write the constant r of the divisor x – r to the left. In this case, r = 2. Bring the first coefficient, 1, down as shown. Example 4

  34. 1 –4 6 –4 2 1 –2 1 –4 6 –4 2 –4 2 1 –2 Synthetic Division Step 3 Multiply the first coefficient by r : 1 ● 2 = 2. Write the product under the second coefficient. Then add the product and the second coefficient: –4 + 2 = –2. Step 4Multiply the sum, –2, by r : –2 ● 2 = –4. Write the product under the next coefficient and add: 6 + (–4) = 2. Example 4

  35. 1 –4 6 –4 4 2 –4 2 0 1 –2 Synthetic Division Step 5 Multiply the sum, 2, by r : 2 ● 2 = 4. Write the product under the next coefficient and add: –4 + 4 = 0. The remainder is 0. The numbers along the bottom are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend. Answer: Example 4

  36. 1 –4 6 –4 4 2 –4 2 0 1 –2 Synthetic Division Step 5 Multiply the sum, 2, by r : 2 ● 2 = 4. Write the product under the next coefficient and add: –4 + 4 = 0. The remainder is 0. The numbers along the bottom are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend. Answer: The quotient is x2 – 2x + 2. Example 4

  37. Use synthetic division to find (x2 + 8x + 7) ÷ (x + 1). A.x + 9 B.x + 7 C.x + 8 D.x + 7 Example 4

  38. Use synthetic division to find (x2 + 8x + 7) ÷ (x + 1). A.x + 9 B.x + 7 C.x + 8 D.x + 7 Example 4

  39. Divisor with First Coefficient Other than 1 Use synthetic division to find (4y3 – 6y2 + 4y – 1) ÷ (2y – 1). Rewrite the divisor so it has a leading coefficient of 1. Divide numerator and denominator by 2. Simplify the numerator and denominator. Example 5

  40. The result is . Divisor with First Coefficient Other than 1 Example 5

  41. Divisor with First Coefficient Other than 1 Answer: Example 5

  42. Answer: The solution is . The result is . Divisor with First Coefficient Other than 1 Check: Divide using long division. 2y2 –2y + 1 4y3 – 2y2 –4y2 + 4y –4y2 + 2y 2y – 1 2y – 1 0  Example 5

  43. A. B. C. D. Use synthetic division to find(8y3 – 12y2 + 4y + 10) ÷ (2y + 1). Example 5

  44. A. B. C. D. Use synthetic division to find(8y3 – 12y2 + 4y + 10) ÷ (2y + 1). Example 5

  45. End of the Lesson

More Related