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 HW: Complete WS Practice 5.2/SGI 5.1 Tabled: Dimensional Analysis pg 227 #56-58, 60 Announcements: Missed Quiz Sect 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!!

Simple Division - dividing a polynomial by a monomial

Simplify

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.

-( ) x x2x2 + 3x - 8x x () x 2 /x = x -8x/x = -8

-( ) h2h2 h3h3 - 4h 2 4h 2 + 4h - 11h 4h h 5h h 3 /h = h h 2 /h = 4h + 5 5h h/h = 5

Synthetic Division - 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. divide a polynomial by a polynomial

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. Since the divisor is x-3, r=

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

Step #5 cont.: Repeat the same procedure Where did 123 and 372 come from?

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

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 1st coefficient. Step#4: Multiply and add. -5 Step#5: Repeat

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

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

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. a x ∙ a y = a x+y Product of powers; add exponents. 2. (a x ) y = a x∙y Power of a power; add exponents. 3. (ab) x = a x b x Power of a product ; Distribute exponent to each term and multiply. 4. (a) x = a x – y Quotient of powers, subtract the exponents. (a) y a cannot equal zero 5. Power of a Quotient b cannot equal 0 6. Zero Exponent 7. Negative Exponents (a) 0 = 1 a -x = 1 a x x x x

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 10 4 )(2x 10 5 ) = 6 x 10 9 Rules for Division in Scientific Notation: 1) Divide the coefficients 2) Subtract the exponents (base 10 remains) Example 1: (6 x 10 6 ) / (2 x 10 3 ) = 3 x 10 3 Exit Ticket 3 rd Period Pg 428 #4-14 evens 5 th /6 th pg 428 #8-15

Scientific Notation: pg 428 #4-7

Notes: Quotient of Powers: (a) m = ∙ a m - n (a) n To divide powers, keep the same base, subtract the exponents. a n 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 a n real numbers a and b, b `(