<span>1)What is f(3) if f(x) = -5x3 + 6x2 - x - 4? a. -74 b. -88 c. 74 d. 182 f(3) = -5(3)^3 + 6(3)^2 - 3 - 4 f(3) = -5(27) + 6(9) - 7 f(3) = -135 + 54 - 7 = -88 (b.) 2)What is f(x + 1) if f(x) = 6x3 - 3x2 + 4x - 9? a. 6x3 + 12x2 + 4x + 2 b. 6x3 + 3x2 + 8x + 6 c. 6x3 + 21x2 + 20x + 4 d. 6x3 + 15x2 + 16x - 2 f(x + 1) = 6(x + 1)^3 - 3(x + 1)^2 + 4(x + 1) - 9 f(x + 1) = 6(x^3 + 3x^2 + 3x + 1) - 3(x^2 + 2x + 1) + 4x + 4 - 9 f(x + 1) = 6x^3 + 18x^2 + 18x + 6 - 3x^2 - 6x - 3 + 4x + 4 - 9 f(x + 1) = 6x^3 + 15x^2 + 16x - 2 (d.) 3)What is 3[f(x + 2)] if f(x) = x3 + 2x2 - 4? a. x3 + 8x2 + 20x + 12 b. 3x3 + 12x2 + 18x + 6 c. 3x3 + 24x2 + 60x + 36 d. 3x3 + 18x2 + 24x + 60 f(x + 2) = (x + 2)^3 + 2(x + 2)^2 - 4 f(x + 2) = x^3 + 6x^2 + 12x + 8 + 2x^2 + 8x + 8 - 4 f(x + 2) = x^3 + 8x^2 + 20x + 12 3[f(x + 2)] = 3x^3 + 24x^2 + 60x + 36 (c.) 4)Use synthetic division to determine which of the following is a factor of x3 - 3x2 - 10x + 24. a. x - 2 b. x - 3 c. x + 4
d. x + 8 2|....1....-3....-10....24 .......1.....-1.....-12....0 (x - 2) works .... (a.) 5)Use synthetic division to determine which of the following is a factor of 2x3 - 13x2 + 17x + 12. a. x - 2 b. x - 3 c. x + 4 d. x + 6 3|....2....-13....17....12 .......2.....-7.....-4....0 (x - 3) is a factor .... (b.) 6)What is the remainder when (6x3 + 9x2 - 6x + 2) ÷ (x + 2)? a. -4 b. 0 c. 2 d. 74 -2|....6....9....-6....2 ..........6.....-3.....0....2 (c.) 7)What is the remainder when (x3 - x2 - 5x - 3) ÷ (x + 1)? a. -8 b. 0 c. 2 d. 4 -1|....1....-1....-5....-3 .........1.....-2.....-3....0 (b.) 8)What are the factors of x3 + 2x2 - x - 2? a. (x - 1)(x + 1)(x - 2) = (x^2 - 1)(x - 2) = x^3 - 2x^2 - x + 2 b. (x - 2)(x + 2)(x - 1) c. (x - 2)(x + 2)(x + 1) d. (x - 1)(x + 1)(x + 2) = (x^2 - 1)(x + 2) = x^3 + 2x^2 - x - 2 (d.)
