Question : Divide using synthetic division. 1) (x^2 + 7x + 10) ÷ (x + 5) : 2153848
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Divide using synthetic division.
1) (x2 + 7x + 10) ÷ (x + 5)
A) x + 2
B) x2 + 2
C) x3 - 5
D) x - 5
2) (x2 + 11x + 15) ÷ (x + 3)
A) x + 8 - (9/x + 3)
B) (x + 8/x + 3)
C) x + 9
D) x + 8 + (9/x + 3)
3) (7x2 + 33x - 54/x + 6)
A) 7x - 9
B) -9x + 6
C) x - 9
D) -7x + 9
4) (-6x3 - 29x2 - 17x + 12/x + 4)
A) - (3/2)x2 - (29/4)x - (17/4)
B) -6x2 - 5x + 3
C) 6x2 + 4x - 3
D) 6x2 - 4x + 3
5) (4x3 + 22x2 - 17x - 30/x + 6)
A) 4x2 x + (11/3) - 5
B) -4x2 - 6x - 5
C) 4x2 - 2x - 5
D) (2/3)x2 + (11/3)x - (17/6)
6) (x5 + x3 - 3/x + 3)
A) x4 - 3x3 + 9x2 - 26x + 78 + (-237/x + 3)
B) x4 - 2 + (3/x + 3)
C) x4 - 2x2 + (3/x + 3)
D) x4 - 3x3 + 10x2 - 30x + 90 + (-273/x + 3)
7) (x4 - 3x3 + x2 + 5x - 7/x - 1)
A) x3 + 2x2 - x + 6 - (3/x - 1)
B) x3 - 2x2 - x + 4 - (3/x - 1)
C) x3 - 2x2 + x + 6 + (6/x - 1)
D) x3 - 2x2 + x + 4 + (6/x - 1)
8) (x4 + 625) ÷ (x - 5)
A) x3+ 5x2 + 25x + 125 + (1250/x - 5)
B) x3+ 5x2 + 25x + 125 + (625/x - 5)
C) x3- 5x2 + 25x - 125 + (1250/x - 5)
D) x3+ 5x2 + 25x + 125
9) (x5 - 3x4 - 8x3 + x2 - x + 18) ÷ (x + 2)
A) x4 - 5x3 + 2x2 - 4x - 6 + (12/x + 2)
B) x4 - 5x3 + 2x2 - 3x + 5 + (8/x + 2)
C) x4 - 5x3 + 2x2 - 4x + 5 + (12/x + 2)
D) x4 - 5x3 + 2x2 - 3x - 5 + (8/x + 2)
10) (5x5 + 2x4 + 2x3 + x2 - x + 5) ÷ (x + 1)
A) 5x4 - 3x3 + 5x2 - 5x + 4 + (6/x + 1)
B) 5x4 - 3x3 + 5x2 - 5x - 4 + (6/x + 1)
C) 5x4 - 3x3 + 5x2 + 4x + 3 + (2/x + 1)
D) 5x4 - 3x3 + 5x2 - 4x - 4 + (2/x + 1)
Use synthetic division and the Remainder Theorem to find the indicated function value.
11) f(x) = x4 - 4x3 + 6x2 - 2x + 9; f(2)
A) -3
B) 13
C) -13
D) 26
12) f(x) = 3x3 - 4x2 - 5x + 4; f(-2)
A) -26
B) -20
C) -22
D) -46
13) f(x) = 4x4 + 10x3 + 2x2 - 6x + 43; f(-2)
A) 103
B) 47
C) 98
D) 81
14) f(x) = x5 - 9x4 - 6x3 + 5; f(-2)
A) -91
B) -27
C) -123
D) 123
15) f(x) = x4 + 6x3 + 8x2 + 6x - 5; f((1/4))
A) - (743/256)
B) - (93/32)
C) - (743/1024)
D) (743/256)
Solve the problem.
16) Use synthetic division to divide f(x) = x3 + 12x2 + 41x + 30 by x + 5. Use the result to find all zeros of f.
A) {5, 6, 1}
B) {-5 , 6, 1}
C) {-5, -6, -1}
D) {5, -6, -1}
17) Solve the equation 2x3 - 17x2 + 31x + 20 = 0 given that 4 is a zero of f(x) = 2x3 - 17x2 + 31x + 20.
A) {4, -5, (1/2)}
B) {4, -1, (5/2)}
C) {4, 1, - (5/2)}
D) {4, 5, - (1/2)}
18) Solve the equation 12x3 - 65x2 + 24x + 10 = 0 given that (2/3) is a root.
A) {(2/3), (1/4), -5}
B) {(2/3), - (5/4), 1}
C) {(2/3), - (1/4), 5}
D) {(2/3), (5/4), -1}
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
19) x3 - 5x2 + 2x + 8 = 0; 2
A) {4, -1, 2}
B) {-4, 1, 2}
C) {-4, -1, 2}
D) {4, 1, 2}
20) 3x3 - 2x2 - 65x + 100 = 0; 4
A) {- (5/3), 5, 4}
B) {(5/3), 5, 4}
C) {(5/3), -5, 4}
D) {- (5/3), -5, 4}
21) 3x3 - 5x2 - 6x + 8 = 0; 1
A) {- (4/3), -2, 1}
B) {(2/3), -4, 1}
C) {(4/3), 2, 1}
D) {- (4/3), 2, 1}
22) 4x3 - 25x2 + 49x - 30 = 0; 2
A) {- (5/4), 3, 2}
B) {(3/4), 5, 2}
C) {(5/4), -3, 2}
D) {(5/4), 3, 2}
Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation.
23) x3 + 6x2 + 11x + 6 = 0
A) -1; The remainder is zero; -1, 2, and -3, or {-3, -1, 2}
B) -1; The remainder is zero; -1, -2, and 3, or {-2, -1, 3}
C) -1; The remainder is zero; 1, -2, and -3, or {-3, -2, 1}
D) -1; The remainder is zero; -1, -2, and -3, or {-3, -2, -1}
24) x3 + 9x2 + 26x + 24 = 0
A) -2; The remainder is zero; 2, -3, and -4, or {-4, -3, 2}
B) -2; The remainder is zero; -2, -3, and -4, or {-4, -3, -2}
C) -2; The remainder is zero; -2, 3, and -4, or {-4, -2, 3}
D) -2; The remainder is zero; -2, -3, and 4, or {-3, -2, 4}
25) 2x3 + 11x2 + 17x + 6 = 0
A) -2; The remainder is zero; -3, 2, and - (1/2), or {-3, - (1/2), 2}
B) -2; The remainder is zero; -3, -2, and (1/2), or {-3, -2, (1/2)}
C) -2; The remainder is zero; -3, -2, and - (1/2), or {-3, -2, - (1/2)}
D) -2; The remainder is zero; 3, -2, and - (1/2), or {-2, - (1/2), 3}
