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Only the numbers are used, no variables Synthetic Division is dividing a polynomial by a binomial (2x2 -1x-3) ÷ (x+1) (2x2-1x-3) ÷ (x+1) The x value that cancels the divisor (-1) is the multiplier The answer (quotient): 2x - 3 (2x2-1x-3) ÷ (x+1) x # remainder The quotient is: (3x3+5x2-2x-120) ÷ (x-3) 3x3+14x2+40x 3x2+14x+40 The quotient (3x3+5x2-2x-120) ÷ (x-3) x2 x 3x2+14x+40 # remainder Quotient: (5x3-6x2+3x+14) ÷(x+1) 5x2-11x+14 5x3-11x2+14x The degree (highest power) of the quotient is ALWAYS one lower than the degree of the dividend Quotient : 5x2-11x+14 (5x3-6x2+3x+14) ÷(x+1) (x2 -3x -10)÷(x-5) Fill in the blanks 5 (x2 -3x -10)÷(x-5) 1 -3 -10 5 (x2 -3x -10)÷(x-5) 1 1 -3 -10 5 (x2 -3x -10)÷(x-5) 1 1 -3 5 -10 5 (x2 -3x -10)÷(x-5) 1 1 -3 5 2 -10 5 (x2 -3x -10)÷(x-5) 1 1 -3 5 2 -10 10 5 (x2 -3x -10)÷(x-5) 1 1 -3 5 2 -10 10 0 The quotient: x2+2 x2+2x x+2 (x3 -4x2 -17x +60)÷(x+4) Fill in the blanks -4 (x3 -4x2 -17x +60)÷(x+4) 1 -4 -17 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -17 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -4 -17 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -4 -8 -17 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -4 -8 -17 32 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -4 -8 -17 15 32 60 -4 (x3 -4x2 -17x +60)÷(x+4) 1 1 -4 -4 -8 -17 15 32 -60 60 -4 Quotient: 1 1 x3-8x2+15x x2-8x+15 -4 -4 -8 -17 15 32 x2-8x x2-8 -60 60 0 The End The End |