Polynomial Division with a Box. Polynomial Multiplication: Area Method x + 5 x 2 x 3 5x25x2 -4x 2 -4x-4x -20x x +1 5 Multiply (x + 5)(x 2 – 4x + 1) x.

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Polynomial Division with a Box

Polynomial Multiplication: Area Method x + 5 x 2 x 3 5x25x2 -4x 2 -4x-4x -20x x +1 5 Multiply (x + 5)(x 2 – 4x + 1) x 3 + x 2 – 19x+ 5 We will reverse this process to divide polynomials. Notice we just proved: Thus the following holds too: Dividend Divisor Quotient

Polynomial Division: Area Method Divide x 4 – 10x 2 + 2x + 3 by x – 3 x 4 +0x 3 –10x 2 +2x + 3 x - 3 x 3 x 4 -3x 3 3x33x3 3x23x2 -9x 2 -x2-x2 -x-x 3x3x -x-x 3 x 3 + 3x 2 – x – 1 Divisor Dividend (make sure to include all powers of x) The sum of these boxes must be the dividend Needed Check Quotient

Polynomial Division Divide 6x 3 + 7x 2 – 16x + 18 by 2x + 5 6x 3 + 7x 2 – 16x x + 5 3x 2 6x36x3 15x 2 -8x 2 -4x -20x 4x4x Rm Sometimes there is a Remainder.