Dividing Polynomials

4.3 Dividing Polynomials Extra Practice In Exercises 1-4, divide using polynomial long division. 1. (x^2 + 6x + 12) ÷ (x - 3) Answer: x + 9 + 39/(x - 3) 2. (x^3 - 4x^2) ÷ (x^2 - 16) Answer: x - 4 + 16/(x + 4) 3. (4x^3 + 13x^2 + 27x + 6) ÷ (4x + 1) Answer: x^2 + 3x + 6 4. (x^4 + 2x^3 + 5x^2 + 3x) ÷ (x^2 - x) Answer: x^2 + 3x + 3 + 11/(x - 1) In Exercises 5-8, divide using synthetic division. 5. (x^2 - 10x + 2) ÷ (x - 2) Answer: x - 8 - 14/(x - 2) 6. (x^3 + 4x^2 + 6x + 4) ÷ (x + 2) Answer: x^2 + 2x + 2 7. (2x^3 - 54) ÷ (x + 3) Answer: 2x^2 - 6x + 18 - 108/(x + 3) 8. (2x^4 - 11x^3 + 11x^2 + 4x + 4) ÷ (x - 4) Answer: 2x^3 - 3x^2 - x + 4 4.3 In Exercises 9-12, match the equivalent expressions. Justify your answers. 9. (x^2 - x - 8) ÷ (x - 4) | 1 -1 -8 | | 4 12 16 | | 1 3 4 | A. x + 3 + 4/(x - 4) 10. (x^2 - x + 8) ÷ (x - 4) | 1 -1 8 | | 4 12 20 | | 1 3 5 | D. x + 5 + 28/(x - 4) 11. (x^2 + x + 8) ÷ (x - 4) | 1 1 8 | | 4 20 112 | | 1 5 28 | C. x + 5 + 28/(x - 4) 12. (x^2 + x + 8) ÷ (x - 4) | 1 1 8 | | 4 20 112 | | 1 5 28 | C. x + 5 + 28/(x - 4) In Exercises 13-16, use synthetic division to evaluate the function for the indicated value of x. 13. f(x) = -3x^3 + 4x^2 - 17x - 6; x = 2 | 2 | -3 4 -17 -6 | | -6 -4 -42 | | -3 -2 -21 -48 | f(2) = -48 14. f(x) = -x^4 + x^2 + 4; x = -1 | -1 | -1 0 1 4 | | 1 -1 0 -4 | | -1 1 0 4 0 | f(-1) = 4 15. f(x) = x^3 - 10x^2 + 31x - 30; x = -5 | -5 | 1 -10 31 -30 | | -5 75 -530 | | 1 -15 106 -560 | f(-5) = -560 16. f(x) = x^3 + 8x + 27; x = 3 | 3 | 1 0 8 27 | | 3 9 51 | | 1 3 17 78 | f(3) = 78