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Do Now: You may not use a calculator!

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Dividing Polynomials

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Simple Division - dividing a polynomial by a monomial

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Simplify

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Long Division - dividing 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.

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

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

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Do Now:

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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. dividing a polynomial by a polynomial

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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

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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=

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

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

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

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

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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

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

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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.

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Step#3: Bring down the 1st coefficient. Step#4: Multiply and add. -5 Step#5: Repeat

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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.

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

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Ex 9: 1 Coefficients

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