AATA Date 111413 SWBAT divide polynomials Do Now

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: Missed Quiz Sect 5. 1 -5. 3 Take afterschool Tutoring: Tues. and Thurs. 3 -4 Winners never quit Math Team T-shirts Quitters never win!! Delivered Tuesday If at first you don’t succeed, Try and try again!!

Simple Division dividing a polynomial by a monomial

Simplify

Simplify

Long Division divide a polynomial by a polynomial • Think back to long division from 3 rd 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.

x- 8 -(x 2 + 3 x) 2 x /x = x - 8 x - 24 -(- 8 x - 24) -8 x/x = -8 0

2 h 3 h /h = 2 h 2 4 h /h -(h 3 + 4 h + 5 - 2 4 h ) 2 4 h 2 - 11 h -(4 h - 16 h) 5 h + 28 = 4 h -(5 h - 20 ) 5 h/h = 5 48

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.

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

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

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

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

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

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

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. 5 15 45 123 372 15 41 124 378

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

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.

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

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.

3

*Remember we cannot have complex fractions we must simplify.

Ex 9: 1 Coefficients

Divide a polynomial by a monomial

Divide a polynomial by a monomial

Steps for Long Division 1. Check 2. Multiply 3. Subtract 4. Bring Down Slide 2 - 26

Two Examples Steps for Long Division 1. Check 2. Multiply 3. Subtract 4. Bring Down

Divide a polynomial by a monomial

Rules of Exponents (Keep same base) 1. ax ∙ ay = ax+y Product of powers; add exponents. 2. (ax )y = ax∙y Power 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)y a cannot equal zero 5. x x x Power of a Quotient b cannot equal 0 6. Zero Exponent (a)0 = 1 7. Negative Exponents a-x = 1 ax

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

Scientific Notation:

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

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

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 a-n = 1 a an Power of a Quotient For any integer m and any real numbers a and b, b