Question 1

Use synthetic division to find the quotient.
-$\frac{x^{4}+7 x^{3}+13 x^{2}+17 x+10}{x+5}$

Accepted Answer

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

Question 2

Use synthetic division to find the quotient.
-$\frac{3 x^{3}-21 x^{2}+28 x+10}{x-5}$

Accepted Answer

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

Question 3

Use synthetic division to decide whether the given number is a solution of the given equation.
-$-3 x^{3}+5 x^{2}+x+33 ; x=3$

Accepted Answer

A) True 
 B)False  True

Question 4

Use synthetic division to decide whether the given number is a solution of the given equation.
-$-x^{4}-3 x^{2}-x+2 ; x=2$

Accepted Answer

A) True 
 B)False

Question 5

Use synthetic division to find the quotient.
-$\frac{x^{5}-1}{x-1}$

Accepted Answer

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)  $x^{5}+x^{4}+x^{3}+x^{2}+x+1+\frac{1}{x-1}$ 
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 decide whether the given number is a solution of the given equation.
-$5 x^{4}-4 x^{2}+4 ; x=\frac{2}{5}$

Accepted Answer

A) True 
 B)False

Question 7

Use synthetic division to decide whether the given number is a solution of the given equation.
-$x^{2}+10 x+34 ; x=-5+3 i$

Accepted Answer

A) True 
 B)False

Question 8

Use synthetic division to decide whether the given number is a solution of the given equation.
-$x^{3}+5 x^{2}+9 x+45 ; x=3 i$

Accepted Answer

A) True 
 B)False

Question 9

Use synthetic division to decide whether the given number is a solution of the given equation.
-$3 x^{4}-46 x^{3}+2 x+1 ; x=\frac{1}{3}$

Accepted Answer

A) True 
 B)False

Question 10

Use synthetic division to find the quotient.
-$\left(3 x^{4}-2 x^{3}-10 x^{2}+15\right) \div(x-2)$

Accepted Answer

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)  $3 x^{3}+4 x^{2}-2 x+4+\frac{-8}{x-2}$ 
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 11

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$k=-2 ; P(x)=3 x^{3}-5 x^{2}-5 x+8$

Accepted Answer

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

Question 12

Use synthetic division to find the quotient.
-$\frac{x^{5}+7 x^{4}+7 x^{3}-12 x^{2}+18 x+17}{x+5}$

Accepted Answer

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

Question 13

Use synthetic division to find the quotient.
-$\left(2 x^{3}+x^{2}-3 x+2\right) \div(x+3)$

Accepted Answer

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)  $2 x^{2}-5 x-12$ 
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 14

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$\mathrm{k}=2+\mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{3}+11$

Accepted Answer

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

Question 15

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$k=2 ; P(x)=3 x^{5}+5 x^{3}+3 x^{2}-2$

Accepted Answer

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

Question 16

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$k=-2 ; P(x)=6 x^{4}+6 x^{3}+4 x^{2}-3 x+24$

Accepted Answer

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

Question 17

Use synthetic division to decide whether the given number is a solution of the given equation.
-$x^{2}-6 x+25 ; x=-3-4 i$

Accepted Answer

A) True 
 B)False

Question 18

Use synthetic division to decide whether the given number is a solution of the given equation.
-$x^{4}-7 x^{2}+6 ; x=1$

Accepted Answer

A) True 
 B)False

Question 19

Use synthetic division to find the quotient.
-$\frac{x^{3}+\frac{7}{3} x^{2}-\frac{7}{3} x-1}{x+\frac{1}{3}}$

Accepted Answer

A)  $x^{2}+2 x-6$ 
B)  $x^{2}-\frac{13}{3} x+\frac{-13}{x+1}$ 
C)  $x^{2}+2 x-3$ 
D)  $x^{2}-\frac{13}{3} x+\frac{14}{9}-\frac{16}{27}$ 
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 20

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$.
-$k=-5 ; P(x)=x^{3}+3 x^{2}+4 x+5$

Accepted Answer

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

Use synthetic division to find the quotient. - $\frac{x^{4}+7 x^{3}+13 x^{2}+17 x+10}{x+5}$

Use synthetic division to find the quotient. - $\frac{3 x^{3}-21 x^{2}+28 x+10}{x-5}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $-3 x^{3}+5 x^{2}+x+33 ; x=3$

Use synthetic division to decide whether the given number is a solution of the given equation. - $-x^{4}-3 x^{2}-x+2 ; x=2$

Use synthetic division to find the quotient. - $\frac{x^{5}-1}{x-1}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $5 x^{4}-4 x^{2}+4 ; x=\frac{2}{5}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{2}+10 x+34 ; x=-5+3 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{3}+5 x^{2}+9 x+45 ; x=3 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $3 x^{4}-46 x^{3}+2 x+1 ; x=\frac{1}{3}$

Use synthetic division to find the quotient. - $\left(3 x^{4}-2 x^{3}-10 x^{2}+15\right) \div(x-2)$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-2 ; P(x)=3 x^{3}-5 x^{2}-5 x+8$

Use synthetic division to find the quotient. - $\frac{x^{5}+7 x^{4}+7 x^{3}-12 x^{2}+18 x+17}{x+5}$

Use synthetic division to find the quotient. - $\left(2 x^{3}+x^{2}-3 x+2\right) \div(x+3)$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $\mathrm{k}=2+\mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{3}+11$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=2 ; P(x)=3 x^{5}+5 x^{3}+3 x^{2}-2$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-2 ; P(x)=6 x^{4}+6 x^{3}+4 x^{2}-3 x+24$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{2}-6 x+25 ; x=-3-4 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{4}-7 x^{2}+6 ; x=1$

Use synthetic division to find the quotient. - $\frac{x^{3}+\frac{7}{3} x^{2}-\frac{7}{3} x-1}{x+\frac{1}{3}}$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-5 ; P(x)=x^{3}+3 x^{2}+4 x+5$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Filters

Exam 13: Appendices

Use synthetic division to find the quotient. - x4+7x3+13x2+17x+10x+5\frac{x^{4}+7 x^{3}+13 x^{2}+17 x+10}{x+5}x+5x4+7x3+13x2+17x+10​

Use synthetic division to find the quotient. - 3x3−21x2+28x+10x−5\frac{3 x^{3}-21 x^{2}+28 x+10}{x-5}x−53x3−21x2+28x+10​

Use synthetic division to decide whether the given number is a solution of the given equation. - −3x3+5x2+x+33;x=3-3 x^{3}+5 x^{2}+x+33 ; x=3−3x3+5x2+x+33;x=3

Use synthetic division to decide whether the given number is a solution of the given equation. - −x4−3x2−x+2;x=2-x^{4}-3 x^{2}-x+2 ; x=2−x4−3x2−x+2;x=2

Use synthetic division to find the quotient. - x5−1x−1\frac{x^{5}-1}{x-1}x−1x5−1​

Use synthetic division to decide whether the given number is a solution of the given equation. - 5x4−4x2+4;x=255 x^{4}-4 x^{2}+4 ; x=\frac{2}{5}5x4−4x2+4;x=52​

Use synthetic division to decide whether the given number is a solution of the given equation. - x2+10x+34;x=−5+3ix^{2}+10 x+34 ; x=-5+3 ix2+10x+34;x=−5+3i

Use synthetic division to decide whether the given number is a solution of the given equation. - x3+5x2+9x+45;x=3ix^{3}+5 x^{2}+9 x+45 ; x=3 ix3+5x2+9x+45;x=3i

Use synthetic division to decide whether the given number is a solution of the given equation. - 3x4−46x3+2x+1;x=133 x^{4}-46 x^{3}+2 x+1 ; x=\frac{1}{3}3x4−46x3+2x+1;x=31​

Use synthetic division to find the quotient. - (3x4−2x3−10x2+15)÷(x−2)\left(3 x^{4}-2 x^{3}-10 x^{2}+15\right) \div(x-2)(3x4−2x3−10x2+15)÷(x−2)

Use the remainder theorem to find P(k)\mathbf{P}(\mathbf{k})P(k) . - k=−2;P(x)=3x3−5x2−5x+8k=-2 ; P(x)=3 x^{3}-5 x^{2}-5 x+8k=−2;P(x)=3x3−5x2−5x+8

Use synthetic division to find the quotient. - x5+7x4+7x3−12x2+18x+17x+5\frac{x^{5}+7 x^{4}+7 x^{3}-12 x^{2}+18 x+17}{x+5}x+5x5+7x4+7x3−12x2+18x+17​

Use synthetic division to find the quotient. - (2x3+x2−3x+2)÷(x+3)\left(2 x^{3}+x^{2}-3 x+2\right) \div(x+3)(2x3+x2−3x+2)÷(x+3)

Use the remainder theorem to find P(k)\mathbf{P}(\mathbf{k})P(k) . - k=2+i;P(x)=x3+11\mathrm{k}=2+\mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{3}+11k=2+i;P(x)=x3+11

Use the remainder theorem to find P(k)\mathbf{P}(\mathbf{k})P(k) . - k=2;P(x)=3x5+5x3+3x2−2k=2 ; P(x)=3 x^{5}+5 x^{3}+3 x^{2}-2k=2;P(x)=3x5+5x3+3x2−2

Use the remainder theorem to find P(k)\mathbf{P}(\mathbf{k})P(k) . - k=−2;P(x)=6x4+6x3+4x2−3x+24k=-2 ; P(x)=6 x^{4}+6 x^{3}+4 x^{2}-3 x+24k=−2;P(x)=6x4+6x3+4x2−3x+24

Use synthetic division to decide whether the given number is a solution of the given equation. - x2−6x+25;x=−3−4ix^{2}-6 x+25 ; x=-3-4 ix2−6x+25;x=−3−4i

Use synthetic division to decide whether the given number is a solution of the given equation. - x4−7x2+6;x=1x^{4}-7 x^{2}+6 ; x=1x4−7x2+6;x=1

Use synthetic division to find the quotient. - x3+73x2−73x−1x+13\frac{x^{3}+\frac{7}{3} x^{2}-\frac{7}{3} x-1}{x+\frac{1}{3}}x+31​x3+37​x2−37​x−1​

Use the remainder theorem to find P(k)\mathbf{P}(\mathbf{k})P(k) . - k=−5;P(x)=x3+3x2+4x+5k=-5 ; P(x)=x^{3}+3 x^{2}+4 x+5k=−5;P(x)=x3+3x2+4x+5

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Filters

Use synthetic division to find the quotient. - $\frac{x^{4}+7 x^{3}+13 x^{2}+17 x+10}{x+5}$

Use synthetic division to find the quotient. - $\frac{3 x^{3}-21 x^{2}+28 x+10}{x-5}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $-3 x^{3}+5 x^{2}+x+33 ; x=3$

Use synthetic division to decide whether the given number is a solution of the given equation. - $-x^{4}-3 x^{2}-x+2 ; x=2$

Use synthetic division to find the quotient. - $\frac{x^{5}-1}{x-1}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $5 x^{4}-4 x^{2}+4 ; x=\frac{2}{5}$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{2}+10 x+34 ; x=-5+3 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{3}+5 x^{2}+9 x+45 ; x=3 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $3 x^{4}-46 x^{3}+2 x+1 ; x=\frac{1}{3}$

Use synthetic division to find the quotient. - $\left(3 x^{4}-2 x^{3}-10 x^{2}+15\right) \div(x-2)$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-2 ; P(x)=3 x^{3}-5 x^{2}-5 x+8$

Use synthetic division to find the quotient. - $\frac{x^{5}+7 x^{4}+7 x^{3}-12 x^{2}+18 x+17}{x+5}$

Use synthetic division to find the quotient. - $\left(2 x^{3}+x^{2}-3 x+2\right) \div(x+3)$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $\mathrm{k}=2+\mathrm{i} ; \mathrm{P}(\mathrm{x})=\mathrm{x}^{3}+11$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=2 ; P(x)=3 x^{5}+5 x^{3}+3 x^{2}-2$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-2 ; P(x)=6 x^{4}+6 x^{3}+4 x^{2}-3 x+24$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{2}-6 x+25 ; x=-3-4 i$

Use synthetic division to decide whether the given number is a solution of the given equation. - $x^{4}-7 x^{2}+6 ; x=1$

Use synthetic division to find the quotient. - $\frac{x^{3}+\frac{7}{3} x^{2}-\frac{7}{3} x-1}{x+\frac{1}{3}}$

Use the remainder theorem to find $\mathbf{P}(\mathbf{k})$ . - $k=-5 ; P(x)=x^{3}+3 x^{2}+4 x+5$