345 3.2 Synthetic Division 3.2 Exercises 3. To perform the division in Exercise 2 using synthetic division, we begin by writing the following. ) 23 4. To perform the division x + 2)x3 + 4x + 2 using synthetic division, we begin by writing the following. )1 42 5. To perform the division x - 3)x3 + 6x2 + 2x using synthetic division, we begin by writing the following. )1 2 6. Consider the following function. ƒ1x2 = 2x4 + 6x3 - 5x2 + 3x + 8 ƒ1x2 = 1x - 2212x3 + 10x2 + 15x + 332 + 74 By inspection, we can state that ƒ122 = . CONCEPT PREVIEWFill in the blank(s) to correctly complete each sentence. 1. In arithmetic, the result of the division 3 5)19 15 4 can be written 19 = 5 # + . 2. In algebra, the result of the division x + 3 x - 1)x2 + 2x + 3 x2 - x 3x + 3 3x - 3 6 can be written x2 + 2x + 3 = 1x - 121 2 + . Use synthetic division to perform each division. See Example 1. 7. x3 + 3x2 + 11x + 9 x + 1 8. x3 + 7x2 + 13x + 6 x + 2 9. 5x4 + 5x3 + 2x2 - x - 3 x + 1 10. 2x4 - x3 - 7x2 + 7x - 10 x - 2 11. x4 + 4x3 + 2x2 + 9x + 4 x + 4 12. x4 + 5x3 + 4x2 - 3x + 9 x + 3 13. x5 + 3x4 + 2x3 + 2x2 + 3x + 1 x + 2 14. x6 - 3x4 + 2x3 - 6x2 - 5x + 3 x + 2 15. -9x3 + 8x2 - 7x + 2 x - 2 16. -11x4 + 2x3 - 8x2 - 4 x + 1 17. 1 3x 3 - 2 9x 2 + 2 27x - 1 81 x - 1 3 18. x3 + x2 + 1 2x + 1 8 x + 1 2
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