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Tuesday, 20181113

Tuesday, 20181113. Essential Questions EQ11: How are polynomials simplified and factored? Word Wall Greatest Common Factor (GCF) Polynomial Monomial Binomial Trinomial Terms. Agenda Bridge Math Store your phones Find your seat Bellwork: ACT Calculator EQ11 Polynomials Exit Ticket

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Tuesday, 20181113

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  1. Tuesday, 20181113 Essential Questions • EQ11: How are polynomials simplified and factored? Word Wall Greatest Common Factor (GCF) Polynomial Monomial Binomial Trinomial Terms Agenda Bridge Math • Store your phones • Find your seat • Bellwork: ACT • Calculator • EQ11 Polynomials • Exit Ticket • Remain in seat until bell rings. Teacher Dismisses NOT the bell. It’s always a great day to be a Wolverine!

  2. Bellwork: Tuesday, ACT.20181113

  3. ACT Question 1

  4. ACT Question 2

  5. ACT Question 3

  6. ACT Question 4

  7. ACT Question 5

  8. ACT Answer KEY G K H A F

  9. The Great Cartoon Scale Drawing Activity Questions Students! Answer the 4 questions on your Cartoon Page. What is the ratio of the original image to your drawing? (Show Calculations) What is the Scale Factor of your original cartoon to the finished scale drawing? (Show your calculations) What is the ratio of the area of the original image to the area of your drawing? Use the large paper measurements and cartoon measurements in centimeters. (Show Your Calculations) In a brief paragraph (5 to 8 complete sentences), describe what you did in The Great Cartoon Scale Drawing Activity and how you know your drawing is similar to the original image.

  10. Vocabulary Greatest Common Factor (GCF) -The highest number that divides exactly into two or more numbers without leaving a remainder. Polynomial - consisting of several terms. Monomial - an algebraic expression consisting of one term. Binomial - an algebraic expression of the sum or the difference of two terms. Trinomial - an algebraic expression of three terms. Terms - are separated by + or − signs.

  11. Review prime factors Write the prime factors of each. • 10ab • 3x2 • 4cd3 • 6y2z2 2●5●a●b 3●x●x 2●2●c●d●d●d 2●3●y●y●z●z

  12. √ EQs for 2nd QuarterRed indicates completed EQ 7. How do we learn about the imaginary unit i and about imaginary numbers like 3i? 8. How do we perform operations with complex numbers? 9. How do we solve problems using properties of multiplication and division solving scientific notation? 10. How do we use algebraic structures to solve proportional reasoning problems? 11. How are polynomials simplified and factored? 12. How do we find zeros of polynomials and graph the function? 15. How do we solve a formula for a given variable, called "solving literal equations"? 17. How are ratios and proportions used to solve problems?

  13. Factoring the GCF from Polynomials

  14. ReviewEQ11 How are polynomials simplified and factored? • Algebraic Factorization is the writing of an expression as the product of prime numbers and variables with no variables having an exponent greater than one.

  15. Example: • 14x2y = 2  7  x  x  y

  16. Steps for Factoring the GCF From Polynomials • Write down the problem. 3x3 + 6x2y – 15xy2

  17. Factoring the GCF From Polynomials • Write down the problem. 3x3 + 6x2y – 15xy2

  18. Steps for Factoring the GCF From Polynomials • Write each term on a separate line and then write the algebraic factorization of each term. 3  x  x  x 3x3 = 6x2y = 2  3  x  x  y 3  5  x  y  y 15xy2=

  19. Steps for Factoring the GCF From Polynomials • “Pair up” all factors that occur in each term and circle them. 3x3 = 3  x  x  x 6x2y =2  3  x  x  y 15xy2 = 3  5  x  y  y

  20. Steps for Factoring the GCF From Polynomials • Multiply what is circled. This is the GCF. When writing the answer, put it outside parenthesis. The “left-overs” for each term should be multiplied and put inside parenthesis.

  21. Step 1 Step 2 3x3 + 6x2y – 15xy2 3x3 = 3  x  x  x 6x2y = 2  3  x  x  y 15xy2 = 3  5  x  y  y Example • Write down the problem. • Write each term on a separate line and then write the algebraic factorization of each term.

  22. Remember exponent rule: Step 3 Example Example • “Pair up” all factors that occur in each term and circle them. Step 3 Step 4 3x3 = 3  x  x  x 6x2y = 2  3  x  x  y 15xy2 = 3  5  x  y  y + – • Multiply what is circled. This is the GCF. When writing the answer, put it outside parenthesis. The “left-overs” for each term should be multiplied and put inside parenthesis. – ) ( 3x x2 + 2xy 5y2

  23. Examples • We will do these together on the board. • 12a2b + 90a2b2c • 32m2n3 – 8m2n + 56m3n2

  24. Examples • We will do these together on the board. • 12a2b + 90a2b2c

  25. Examples • We will do these together on the board. • 32m2n3 – 8m2n + 56m3n2

  26. Try these yourself. • 15x2 – 20xy • 3x2 + 15x • 20abc + 15a2c – 5ac

  27. Partners • Take out a sheet of paper. Label the paper EQ11 GCF, Name, Date, Classperiod • Please find your working partner quietly and quickly.

  28. and rewrite the problems with GCF and leftovers in parenthesis

  29. and rewrite the problems with GCF and leftovers in parenthesis

  30. Exit Ticket • 10a3bc2(4a2b2c – 3a2bc3) • What exponent rule allows you to combine the exponents? Explain how to combine exponents according to the exponent rule.

  31. Extra GCF on next 2 slides

  32. RULES FOR EXPONENTS(all numbers below must be real) Remember: EXPONENT RULES

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