5.5a – Long Division.

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Presentation transcript:

5.5a – Long Division

When using long division, make sure to write the expression in descending order and use a place holder for missing terms. Ex. What is the missing term? 5x5 + 2x4 - 3x3 – 5x + 1 0x2

Divide using long division. 1. (x2 – 2x – 48)  (x + 5) x x + 5 x2 – 2x – 48 –( ) x2 + 5x

Divide using long division. 1. (x2 – 2x – 48)  (x + 5) x – 7 13 . x + 5 x + 5 x2 – 2x – 48 x – 7 – – – x2 + 5x – 7x – 48 –7x – 35 – 13

Divide using long division. 2. (x3 – x2 + 4x – 10)  (x + 2) x2 – 3x + 10 30 . x + 2 x + 2 x3 – x2 + 4x – 10 x2 – 3x + 10 – – – x3 + 2x2 – 3x2 + 4x –3x2 – 6x 10x – 10 10x + 20 – 30

Divide using long division. 3. (x4 – 7x2 + 9x – 10)  (x – 2) x3 + 2x2 – 3x + 3 x – 2 x4 + 0x3 – 7x2 + 9x – 10 x4 – 2x3 2x3 –7x2 4 . x – 2 2x3 –4x2 x3 + 2x2 – 3x + 3 – –3x2 + 9x –3x2 + 6x 3x – 10 3x – 6 – 4

Divide using long division. 4. (5x4 + 2x3 – 9x + 12)  (x2 – 3x + 4) 16x – 112. x2 – 3x + 4 5x2 + 17x + 31 + 5x2 + 17x + 31 x2 – 3x + 4 5x4 + 2x3 + 0x2 – 9x + 12 5x4 –15x3 +20x2 17x3 – 20x2 – 9x 17x3 –51x2 +68x 31x2 –77x +12 31x2 –93x +124 16x –112

5. f(x) = x3 – 3x2 – 16x – 12; x – 6 x2 + 3x + 2 (x – 6)(x2 + 3x + 2) Given polynomial f(x) and a factor of f(x), factor f(x) completely. 5. f(x) = x3 – 3x2 – 16x – 12; x – 6 x2 + 3x + 2 (x – 6)(x2 + 3x + 2) x – 6 x3 – 3x2 – 16x – 12 x 2 x3 – 6x2 x 1 3x2 – 16x 2x + x 3x2 –18x 2x – 12 (x – 6)(x + 2)(x + 1) 2x – 12

Given polynomial f(x) and a factor of f(x), factor f(x) completely. 6. f(x) = x3 – 18x2 + 95x – 126; x – 9 x2 – 9x + 14 (x – 9)(x2 – 9x + 14) x – 9 x3 – 18x2 + 95x – 126 x –7 x3 – 9x2 x –2 – 9x2 + 95x –7x + –2x – 9x2 + 81x 14x – 126 (x – 9)(x – 7)(x – 2) 14x – 126