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Polynomial Division with a Box

Polynomial Division with a Box. Polynomial Multiplication: Area Method. Multiply ( x + 5)( x 2 – 4 x + 1) . We will reverse this process to divide polynomials. x 2. - 4 x. +1. Notice we just proved:. x. x 3. -4 x 2. x. Thus the following holds too:. + 5. 5 x 2. -20 x. 5.

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Polynomial Division with a Box

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  1. Polynomial Division with a Box

  2. Polynomial Multiplication: Area Method Multiply (x + 5)(x2 – 4x + 1) We will reverse this process to divide polynomials. x2 -4x +1 Notice we just proved: x x3 -4x2 x Thus the following holds too: + 5 5x2 -20x 5 x3 + x2 – 19x + 5 Quotient Dividend Divisor

  3. Polynomial Division: Area Method Divide x4 – 10x2 + 2x + 3 by x – 3 Quotient x3 3x2 -x -1 Dividend (make sure to include all powers of x) x x4 3x3 -x2 -x The sum of these boxes must be the dividend Divisor - 3 -3x3 -9x2 3x 3 x4 +0x3 –10x2 +2x + 3 Needed Needed Needed Check Needed x3 + 3x2 – x – 1

  4. Polynomial Division Divide 6x3 + 7x2 – 16x + 18 by 2x + 5 3x2 -4x 2 Rm Sometimes there is a Remainder. 2x 6x3 -8x2 4x 8 + 5 15x2 -20x 10 6x3 + 7x2 – 16x + 18

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