Deck 13: Appendices

Question 1

Use synthetic division to find the quotient.

- $\frac{3 x^{3}-21 x^{2}+28 x+10}{x-5}$

A) $-3 x^{2}+5 x-2$
B) $3 x^{2}-6 x-2$
C) $3 x-6$
D) $\frac{3}{5} x^{2}+-\frac{21}{5} x+\frac{28}{5}$

Answer 1

$3 x^{2}-6 x-2$

Question 2

Use synthetic division to find the quotient.

- $\frac{x^{4}+7 x^{3}+13 x^{2}+17 x+10}{x+5}$

A) $x^{3}+2 x^{2}+6 x$
B) $x^{3}+2 x^{2}+6 x+4$
C) $x^{3}+3 x^{2}+3 x-2$
D) $x^{3}+2 x^{2}+3 x+2$

Answer 2

$x^{3}+2 x^{2}+3 x+2$

Question 3

Use synthetic division to find the quotient.

- $\frac{x^{5}+7 x^{4}+7 x^{3}-12 x^{2}+18 x+17}{x+5}$

A) $x^{4}+2 x^{3}-3 x^{2}+3 x+2$
B) $x^{4}+2 x^{3}-3 x^{2}+3 x+3+\frac{2}{x+5}$
C) $x^{3}+2 x^{2}-3 x+3+\frac{2}{x+5}$
D) $x^{4}+2 x^{3}-3 x^{2}+3 x-3+\frac{4}{x+5}$

Answer 3

$x^{4}+2 x^{3}-3 x^{2}+3 x+3+\frac{2}{x+5}$

Question 4

Use synthetic division to find the quotient.

- $\frac{x^{3}+\frac{7}{3} x^{2}-\frac{7}{3} x-1}{x+\frac{1}{3}}$

A) $x^{2}+2 x-6$
B) $x^{2}-\frac{13}{3} x+\frac{-13}{x+1}$
C) $x^{2}+2 x-3$
D) $x^{2}-\frac{13}{3} x+\frac{14}{9}-\frac{16}{27}$

Question 5

Use synthetic division to find the quotient.

- $\frac{x^{5}-1}{x-1}$

A) $x^{4}+x^{3}+x^{2}+x+1+\frac{1}{x-1}$
B) $x^{4}+x^{3}+x^{2}+x+1$
C) $x^{5}+x^{4}+x^{3}+x^{2}+x+1$
D) $x^{5}+x^{4}+x^{3}+x^{2}+x+1+\frac{1}{x-1}$

Question 6

Use synthetic division to find the quotient.

- $\left(-6 x^{3}+2 x^{2}+5 x-10\right) \div(x-2)$

A) $-6 x^{2}-10 x-15+\frac{-40}{x-2}$
B) $-6 x^{2}-10 x-5+\frac{-10}{x-2}$
C) $-6 x^{2}-10 x-25+\frac{-40}{x-2}$
D) $-6 x^{2}-10 x-15+\frac{-25}{x-2}$

Question 7

Use synthetic division to find the quotient.

- $\left(x^{4}+256\right) \div(x-4)$

A) $x^{3}+4 x^{2}+16 x+64$
B) $x^{3}-4 x^{2}+16 x-64+\frac{512}{x-4}$
C) $x^{3}+4 x^{2}+16 x+64+\frac{512}{x-4}$
D) $x^{3}+4 x^{2}+16 x+64+\frac{256}{x-4}$

Question 8

Use synthetic division to find the quotient.

- $\left(2 x^{3}+x^{2}-3 x+2\right) \div(x+3)$

A) $2 x^{2}-5 x-12+\frac{-34}{x+3}$
B) $2 x^{2}-5 x+12$
C) $2 x^{2}-5 x+12+\frac{-34}{x+3}$
D) $2 x^{2}-5 x-12$

Question 9

Use synthetic division to find the quotient.

- $\left(3 x^{4}-2 x^{3}-10 x^{2}+15\right) \div(x-2)$

A) $3 x^{3}+4 x^{2}-x-3+\frac{1}{x-2}$
B) $3 x^{3}+4 x^{2}-2 x-4+\frac{7}{x-2}$
C) $3 x^{3}+4 x^{2}-2 x-4+\frac{-11}{x-2}$
D) $3 x^{3}+4 x^{2}-2 x+4+\frac{-8}{x-2}$

Question 10

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=-2 ; P(x)=3 x^{3}-5 x^{2}-5 x+8$

A) -26
B) -46
C) -22
D) -20

Question 11

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=-2 ; P(x)=6 x^{4}+6 x^{3}+4 x^{2}-3 x+24$

A) 98
B) 94
C) 100
D) -98

Question 12

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=3 ; P(x)=x^{2}-3 x-5$

A) 5
B) -23
C) -5
D) -13

Question 13

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $\mathrm{k}=-3 ; \mathrm{P}(\mathrm{x})=-\mathrm{x}^{3}+2 \mathrm{x}^{2}-2$

A) 43
B) -6
C) -46
D) -43

Question 14

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=-5 ; P(x)=x^{3}+3 x^{2}+4 x+5$

A) 180
B) -75
C) 185
D) -65

Question 15

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=2 ; P(x)=3 x^{5}+5 x^{3}+3 x^{2}-2$

A) 146
B) 147
C) -122
D) -126

Question 16

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $k=-2 ; P(x)=x^{6}+2 x^{5}+2 x^{4}+3 x^{3}-3 x^{2}-4 x-6$

A) -1
B) 2
C) -2
D) 158

Question 17

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $\mathrm{k}=\frac{1}{2} ; \mathrm{P}(\mathrm{x})=-8 \mathrm{x}^{3}+16 \mathrm{x}^{2}-8 \mathrm{x}$

A) 2
B) -2
C) -1
D) 0

Question 18

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $\mathrm{k}=2+\mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{3}+11$

A) $13+12 i$
B) $13+11 \mathrm{i}$
C) $2+11 \mathrm{i}$
D) $2+12 \mathrm{i}$

Question 19

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ .

- $\mathrm{k}=4-2 \mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{2}-2 \mathrm{x}+4$

A) $8-12 \mathrm{i}$
B) -4
C) $8-4 \mathrm{i}$
D) $4-4 \mathrm{i}$

Question 20

Use synthetic division to decide whether the given number is a solution of the given equation.

- $-3 x^{3}+5 x^{2}+x+33 ; x=3$

Question 21

Use synthetic division to decide whether the given number is a solution of the given equation.

- $-7 x^{3}+x^{2}+3 x-1 ; x=2$

Question 22

Use synthetic division to decide whether the given number is a solution of the given equation.

- $x^{4}-7 x^{2}+6 ; x=1$

Question 23

Use synthetic division to decide whether the given number is a solution of the given equation.

- $-x^{4}-3 x^{2}-x+2 ; x=2$

Question 24

Use synthetic division to decide whether the given number is a solution of the given equation.

- $3 x^{4}-46 x^{3}+2 x+1 ; x=\frac{1}{3}$

Question 25

Use synthetic division to decide whether the given number is a solution of the given equation.

- $5 x^{4}-4 x^{2}+4 ; x=\frac{2}{5}$

Question 26

Use synthetic division to decide whether the given number is a solution of the given equation.

- $x^{2}+10 x+34 ; x=-5+3 i$

Question 27

Use synthetic division to decide whether the given number is a solution of the given equation.

- $x^{2}-6 x+25 ; x=-3-4 i$

Question 28

Use synthetic division to decide whether the given number is a solution of the given equation.

- $x^{3}+5 x^{2}+9 x+45 ; x=3 i$

Question 29

Use synthetic division to decide whether the given number is a solution of the given equation.

- $x^{3}+7 x^{2}-16 x+18 ; x=2+i$