Goal: to divide polynomials using LONG and SYNTHETIC methods.

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Presentation transcript:

Goal: to divide polynomials using LONG and SYNTHETIC methods. 11.3 Dividing Polynomials Goal: to divide polynomials using LONG and SYNTHETIC methods. Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Remember: Long Division: without a calculator we can divide the following 4 9 - 92 21 2 - 207 Keep going and Finish!! 5 Answer: 49251 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

When Dividing Polynomials: This long division technique can also be used to divide polynomials Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Divide: - x² +3x -18 / (x-3) - x + 6 R 0 x - 3 x2 + 3x - 18 ( x2 - 3x - 18 - ( 6x - 18 ) Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Divide: - x² +3x -18 / (x-3) - -16 2x - 3 R : -16 x - 8 2x2 - 19x + 8 + 8 - ( - 3x + 24 ) -16 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Divide: - - (5x³ -13x² +10x -8) / (x-2) - 5x² - 3x + 4 R: 0 x - 2 + 4 R: 0 x - 2 5x³ - 13x² + 10x - 8 - ( 5x³ - 10x² ) -3x² + 10x - ( -3x² + 6x ) 4x - 8 - ( 4x - 8 ) Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

So in other words… 5x³ -13x² +10x - 8 x-2 OR 5x³ -13x² +10x - 8 = x-2 OR 5x³ -13x² +10x - 8 = (5x² -3x + 4) (x-2) Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

When Dividing Polynomials: SYNTHETIC division uses the coefficients of each term. Make sure you include the zeros for the powers that are not present. Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Synthetic division (5x³ -13x² +10x -8) / (x-2) Opposite of number in divisor x³ x² x x0 Use the coefficients of each term. 2 5 -13 10 -8 10 -6 8 5 -3 4 Start with one power less than the original equations. 5x² -3x + 4 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Synthetic division (2w³ +3w -15) / (w-1) Opposite of number in divisor w³ w² w w0 Use the coefficients of each term. 1 2 0 3 -15 2 2 5 Notice: -10 is the remainder. 2 2 5 -10 Start with one power less than the original equations. 2w² + 2w + 5 - 10/(w-1) Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

Synthetic division: (x³ -13x +12 ) / (x+4) x2 -4x + 3 1 0 -13 12 Use the coefficients of each term. Include the ones not present  0x2 Opposite of number in divisor x³ x² x x0 -4 1 0 -13 12 -4 +16 -12 1 -4 3 Start with one power less than the original equations. x2 -4x + 3 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

A Couple of Notes Use synthetic division when the coefficient in front of x is 1 (x- 2) (2x-3) YES NO To test so see if a binomial is a factor, you want to see if you get a remainder of zero. If yes, it is a factor. If you get a remainder, the answer is no. Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

In this case, x-3 is not a factor because there was a remainder of 6 + 6 R 6 x - 3 2x² -19x - ( x² - 3x ) 6x -12 - ( 6x - 18 ) 6 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

From this example, x-8 IS a factor because the remainder is zero (2x² -19x + 8) / (x-8) 2x - 1 R: 0 x - 8 2x² - 19x + 8 -( 2x² - 18x ) - x + 8 - ( x + 8 ) Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1

In this case, x-3 is not a factor because there was a remainder of 6 + 6 R 6 x - 3 x² + 3x - 12 - ( x² - 3x ) 6x -12 - ( 6x - 18 ) 6 Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1