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Dividing Polynomials Monomials (Ex: 2x): It divides into everything…

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A) (15x 3 - 10x 2 + 5x -10) / (5x) 15x 3 - 10x 2 + 5x -10 __ 5x 3x 2 - 2x + 1 – 2 x

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(4x 3 y 3 -8xy 2 -12x 2 y 3 ) (-4x 3 y 3 ) -1 4x 3 y 3 -8xy 2 - 12x 2 y 3 _____ -4x 3 y 3 _____ -4x 3 y 3 _____ -4x 3 y 3 -1 + 2+ 3 x 2 y x -1 exponent means to put it in the denominator 4x 3 y 3 -8xy 2 -12x 2 y 3 -4x 3 y 3

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Dividing Polynomials Polynomials (ex: x+2): LONG DIVISION…

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Remainder Reminder 17/3 is 5 R 2 5 + 2 3 153/13 is 11 R 10 11 + 10 13 x 2 +6x+3 is x+4 R -5 x+4 + -5x+2

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_____ 52)25341 487+ 17 52 208 45 416 4 38 364 17 - - 1 - Divide Multiply Subtract (draw line change sign) Carry

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Multiply 6 by x-4 X 2 + 2x – 24 x – 4 __________ x-4 )X 2 + 2x – 24 +6 X2X2 - - 0 + 6x - 24 x 6x - 24 - - 0 Divide Multiply Subtract (draw the line change the sign, add) Carry Answer: X + 6 No remainder so x+6 only x-4 is a binomial….. Yes, you can factor/cancel but also show long division How many times does x go into x 2 ? How many times does x go into 6x? FYI: (x+6)(x–4) (x – 4) Gives (x+6) Divide Multiply x by x-4 Subtract (draw the line, change the sign, add) Carry Subtract (draw the line, change the sign, add) - 4x + +

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One-thousand twenty-five is 1025 So x 3 – 2x 2 + 1 is: X 3 – 2x 2 + 0x + 1

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x 4 + x 2 – 3x + 5 x 2 + 2x + 3 __________________ X 2 + 2x + 3 )1x 4 + 0x 3 +1x 2 –3x +5 x 2 x 4 +2x 3 +3x 2 - - - 0 - 2x 3 -2x 2 -2x 3 - 4x 2 – 6x - - - 0 +2x 2 + 3x +2x 2 + 4x +6 - - - -x -1 Answer: x 2 –2x+2+ -x-1 x 2 +2x+3 -2 x +2 Divide -2x 3 by x 2 Divide x 4 by x 2 Multiply x 2 + 2x + 3 by x 2 Subtract (draw the line, change the sign, add) Carry Subtract (draw the line, change the sign, add) – 3x Multiply x 2 + 2x + 3 by -2x +5 Carry Divide 2x 2 by x 2 Multiply x 2 + 2x + 3 by 2 Subtract (draw the line, change the sign, add)

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Unit 2: Algebra Lesson 1 – Introduction to Polynomials Learning Goals: I can simplify polynomial expressions.

Unit 2: Algebra Lesson 1 – Introduction to Polynomials Learning Goals: I can simplify polynomial expressions.

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