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

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

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

(4x 3 y 3 -8xy 2 -12x 2 y 3 ) (-4x 3 y 3 ) -1 4x 3 y 3 -8xy x 2 y 3 _____ -4x 3 y 3 _____ -4x 3 y 3 _____ -4x 3 y 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

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

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

_____ 52) Divide Multiply Subtract (draw line change sign) Carry

Multiply 6 by x-4 X 2 + 2x – 24 x – 4 __________ x-4 )X 2 + 2x – X2X x - 24 x 6x 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 + +

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

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 x 3 -2x 2 -2x 3 - 4x 2 – 6x x 2 + 3x +2x 2 + 4x 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)