3y-5 = -1
3y=4
y = 4/3
3y-5 = 1
3y = 6
y = 2
y must be between 4/3 and 2
y must be between 1 1/3 and 2
<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.)
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