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AAT-A Date : 11/14/13 SWBAT divide polynomials. Do Now: ACT Prep Problems

AAT-A Date : 11/14/13 SWBAT divide polynomials. Do Now: ACT Prep Problems HW Requests: Math 11 Worksheet Start Vocab sheet In class: Worksheets to look at 5.1-5.3 HW : Complete WS Practice 5.2/SGI 5.1 Tabled: Dimensional Analysis pg 227 #56-58, 60 Announcements :

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AAT-A Date : 11/14/13 SWBAT divide polynomials. Do Now: ACT Prep Problems

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  1. AAT-A • Date:11/14/13 SWBAT divide polynomials. • Do Now: ACT Prep Problems • HW Requests: Math 11 Worksheet • Start Vocab sheet • In class: Worksheets to look at 5.1-5.3 • HW: Complete WS Practice 5.2/SGI 5.1 • Tabled: Dimensional Analysis pg227 #56-58, 60 • Announcements: • Missed Quiz Sect 5.1-5.3 Take afterschool • Tutoring: Tues. and Thurs. 3-4 • Math Team T-shirts • Delivered Tuesday Winners never quit Quitters never win!! If at first you don’t succeed, Try and try again!!

  2. Simple Division - dividing a polynomial by a monomial

  3. Simplify

  4. Simplify

  5. Long Division - divide a polynomial by a polynomial • Think back to long division from 3rd grade. • How many times does the divisor go into the dividend? Put that number on top. • Multiply that number by the divisor and put the result under the dividend. • Subtract and bring down the next number in the dividend. Repeat until you have used all the numbers in the dividend.

  6. x2/x = x -8x/x = -8 x - 8 + 3x -( ) x2 - 8x - 24 -( ) - 8x - 24 0

  7. h3/h = h2 4h2/h = 4h 5h/h = 5 h2 + 4h + 5 -( ) - 4h2 h3 - 11h 4h2 -( ) 4h2 - 16h 5h + 28 -( ) 5h - 20 48

  8. Synthetic Division - divide a polynomial by a polynomial • To use synthetic division: • There must be a coefficient for every possible power of the variable. • The divisor must have a leading coefficient of 1.

  9. Since the numerator does not contain all the powers of x, you must include a 0 for the Step #1: Write the terms of the polynomial so the degrees are in descending order.

  10. 5 0 -4 1 6 Step #2: Write the constant r of the divisor x-r to the left and write down the coefficients. Since the divisor is x-3, r=3

  11. 5 Step #3: Bring down the first coefficient, 5.

  12. Step #4: Multiply the first coefficient by r, so and place under the second coefficient then add. 15 5 15

  13. 15 45 15 5 Step #5: Repeat process multiplying the sum, 15, by r; and place this number under the next coefficient, then add. 41

  14. 15 45 123 372 15 41 5 Step #5 cont.: Repeat the same procedure. Where did 123 and 372 come from? 124 378

  15. 15 45 123 372 15 41 124 378 5 Step #6: Write the quotient. The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend.

  16. The quotient is: Remember to place the remainder over the divisor.

  17. Ex 7: Step#1: Powers are all accounted for and in descending order. Step#2: Identify r in the divisor. Since the divisor is x+4, r=-4 .

  18. Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. Step#5: Repeat. 4 -4 20 0 8 -1 1 0 -2 10 -5

  19. Ex 8: Notice the leading coefficient of the divisor is 2 not 1. We must divide everything by 2 to change the coefficient to a 1.

  20. 3

  21. *Remember we cannot have complex fractions - we must simplify.

  22. Ex 9: Coefficients 1

  23. Divide a polynomial by a monomial

  24. Divide a polynomial by a monomial

  25. Steps for Long Division Check Multiply Subtract Bring Down

  26. Two Examples Steps for Long Division Check Multiply Subtract Bring Down

  27. Divide a polynomial by a monomial

  28. Rules of Exponents (Keep same base) • 1. ax ∙ ay = ax+yProduct of powers; add exponents. • 2. (ax )y = ax∙yPower of a power; add exponents. • 3. (ab)x= ax bx Power of a product ; Distribute exponent to each term and multiply. • 4. (a)x= ax – y Quotient of powers, subtract the exponents. • (a)ya cannot equal zero • 5. Power of a Quotient • b cannot equal 0 • 6. Zero Exponent 7. Negative Exponents • (a)0 = 1 a-x = 1 • ax x x x

  29. Scientific Notation: Way to represent VERY LARGE numbers. Standard Notation: Decimal Form

  30. Scientific Notation:

  31. Rules for Multiplication in Scientific Notation: 1) Multiply the coefficients 2) Add the exponents (base 10 remains) Example 1: (3 x 104)(2x 105) = 6 x 109 Exit Ticket 3rd Period Pg 428 #4-14 evens 5th/6th pg 428 #8-15 Rules for Division in Scientific Notation: 1) Divide the coefficients 2) Subtract the exponents (base 10 remains) Example 1: (6 x 106) / (2 x 103) = 3 x 103

  32. Scientific Notation: http://ostermiller.org/calc/calculator.html pg 428 #4-7

  33. Notes:Quotient of Powers: • (a)m= ∙ am - n • (a)n • To divide powers, keep the same base, subtract the exponents. an cannot equal zero • Zero Exponent • (a)0 = 1 a • Negative Exponents Power of a Quotient • a-n = 1 a For any integer m and any • anreal numbers a and b, b • `(

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