SOLUTION: Please im asking for some help with the following promblems. You guys have really helped me over summer.Thank you'll for your dedication to helping others. 1)What is f(3) if f(x

Question 48414: Please im asking for some help with the following promblems. You guys have really helped me over summer.Thank you'll for your dedication to helping others.
1)What is f(3) if f(x) = -5x3 + 6x2 - x - 4?
a. -74
b. -88
c. 74
d. 182
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
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
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
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
6)What is the remainder when (6x3 + 9x2 - 6x + 2) � (x + 2)?
a. -4
b. 0
c. 2
d. 74
7)What is the remainder when (x3 - x2 - 5x - 3) � (x + 1)?
a. -8
b. 0
c. 2
d. 4
8)What are the factors of x3 + 2x2 - x - 2?
a. (x - 1)(x + 1)(x - 2)
b. (x - 2)(x + 2)(x - 1)
c. (x - 2)(x + 2)(x + 1)
d. (x - 1)(x + 1)(x + 2)
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
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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