PRACTICE Use long division to divide. SEE EXAMPLE 1 15. x3 + 5x2 - x - 5 divided by x - 1 16. 2x3 + 9x2 + 10x + 3 divided by 2x + 1 17. 3x3 - 2x2 + 7x + 9 divided by x2 - 3x 18. 2x4 - 6x2 + 3 divided by 2x - 6 Use synthetic division to divide. SEE EXAMPLE 2 19. x4 - 25x2 + 144 divided by x - 4 20. x3 + 6x2 + 3x - 10 divided by x + 5 21. x5 + 2x4 - 3x3 + x - 1 divided by x + 2 22. -x4 + 7x3 + x2 - 2x - 12 divided by x - 3 23. Use synthetic division to show that the remainder of f(x) = x4 - 6x3 - 33x2+ 46x + 75 divided by x - 9 is P(9). SEE EXAMPLE 3 q s smer erdt is x Toaivib Use the Remainder Theorem to evaluate each polynomial for the given value of X. SEE EXAMPLE 4 24. f (x) = x3 + 9x2+ 3x - 7; x=-5 25. f(x) = 2x3 - 3x2 + 4x + 13; x=3 26. f(x) =-x4+ 2x3 - x2 + 4x+8;x=-2 anid erT 27. f(x) = x5 - 3x4 - 2x3 + x2 - 2x - 1; x = 4 o bris Is each given binomial a factor of the given polynomial? If so, write the polynomial as a product of two factors. SEE EXAMPLE 5 28. polynomial: P(x) = 8x3 - 10x2 + 28x - 16; not binomial: x - 3 29. polynomial: P(x) = 4x4 - 9x3 - 7x2 - 2x + 25; binomial: x + 4 30. polynomial: P(x) = -x5 + 12x3 + 6x2 - 23x + 1; binomial: x - 2 31. polynomial: P(x) = 2x3 + 3x2 - 8x - 12; binomial: 2x + 3