Question 1

Use synthetic division to find the quotient and the remainder. $\frac { 5 x ^ { 2 } + 2 x - 1 } { x - 1 }$

Accepted Answer

A)  $\text { quotient: } - 6 x + 5 \text {; remainder: } - 7$ 
B)  $\text { quotient: } 5 x + 7 \text {; remainder: } 6$ 
C)  $\text { quotient: } 7 x + 6 \text {; remainder: } 7$ 
D)  $\text { quotient: } 7 x - 5 \text {; remainder: } 6$ 
E)  $\text { quotient: } 5 x + 7 \text {; remainder: } - 8$ 
A)  $\text { quotient: } - 6 x + 5 \text {; remainder: } - 7$ 
B)  $\text { quotient: } 5 x + 7 \text {; remainder: } 6$ 
C)  $\text { quotient: } 7 x + 6 \text {; remainder: } 7$ 
D)  $\text { quotient: } 7 x - 5 \text {; remainder: } 6$ 
E)  $\text { quotient: } 5 x + 7 \text {; remainder: } - 8$

Question 2

One root of the equation is given. Determine the remaining roots. $x ^ { 3 } - 9 x ^ { 2 } + 28 x - 40 = 0 ; x = 2 + 2 i$

Accepted Answer

A)  $x = 2 + 2 i , 4$ 
B)  $x = 2 - 2 i , - 5$ 
C)  $x = 2 + 2 i , - 5$ 
D)  $x = 2 - 2 i , 5$ 
E)  $x = 2 + 2 i , 9$ 
A)  $x = 2 + 2 i , 4$ 
B)  $x = 2 - 2 i , - 5$ 
C)  $x = 2 + 2 i , - 5$ 
D)  $x = 2 - 2 i , 5$ 
E)  $x = 2 + 2 i , 9$

Question 3

Find the rational roots and solve the equation. 4x 3  - 10x 2  - 25x + 4 = 0

Accepted Answer

A)  $\frac { - 3 \pm \sqrt { 13 } } { 2 } , 4$ 
B)  $\frac { - 3 \pm \sqrt { 15 } } { 4 } , 4$ 
C)  $\frac { - 3 \pm \sqrt { 13 } } { 4 } , - 4$ 
D)  $\frac { - 3 \pm \sqrt { 13 } } { 4 } , 4$ 
E)  $\frac { 3 \pm \sqrt { 13 } } { 4 } , 4$ 
A)  $\frac { - 3 \pm \sqrt { 13 } } { 2 } , 4$ 
B)  $\frac { - 3 \pm \sqrt { 15 } } { 4 } , 4$ 
C)  $\frac { - 3 \pm \sqrt { 13 } } { 4 } , - 4$ 
D)  $\frac { - 3 \pm \sqrt { 13 } } { 4 } , 4$ 
E)  $\frac { 3 \pm \sqrt { 13 } } { 4 } , 4$

Question 4

Determine which of the following real numbers is a root of the equation. $12 x - 8 = 136$

Accepted Answer

A)  $x = \frac { 8 } { 12 }$ 
B)  $x = 12$ 
C)  $x = 20$ 
D)  $x = 14$ 
E)  $x = 0$ 
A)  $x = \frac { 8 } { 12 }$ 
B)  $x = 12$ 
C)  $x = 20$ 
D)  $x = 14$ 
E)  $x = 0$

Question 5

The equation has exactly one positive root. Locate the root between successive hundredths. 
x 3  - 3x 2  + 3x - 12 = 0

Accepted Answer

A)  between 3.11 and 3.12 
B)  between 4.31 and 4.32 
C)  between 2.22 and 2.23 
D)  between 3.22 and 3.23 
E)  between 2.02 and 2.03 
A)  between 3.11 and 3.12 
B)  between 4.31 and 4.32 
C)  between 2.22 and 2.23 
D)  between 3.22 and 3.23 
E)  between 2.02 and 2.03

Use synthetic division to find the quotient and the remainder. $\frac { 5 x ^ { 2 } + 2 x - 1 } { x - 1 }$

One root of the equation is given. Determine the remaining roots. $x ^ { 3 } - 9 x ^ { 2 } + 28 x - 40 = 0 ; x = 2 + 2 i$

Find the rational roots and solve the equation. 4x³ - 10x² - 25x + 4 = 0

Determine which of the following real numbers is a root of the equation. $12 x - 8 = 136$

The equation has exactly one positive root. Locate the root between successive hundredths. x³ - 3x² + 3x - 12 = 0

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Additional Topics in Algebra

Filters

Exam 13: Roots of Polynomial Equations

Use synthetic division to find the quotient and the remainder. 5x2+2x−1x−1\frac { 5 x ^ { 2 } + 2 x - 1 } { x - 1 }x−15x2+2x−1​

One root of the equation is given. Determine the remaining roots. x3−9x2+28x−40=0;x=2+2ix ^ { 3 } - 9 x ^ { 2 } + 28 x - 40 = 0 ; x = 2 + 2 ix3−9x2+28x−40=0;x=2+2i

Find the rational roots and solve the equation. 4x 3 - 10x 2 - 25x + 4 = 0

Determine which of the following real numbers is a root of the equation. 12x−8=13612 x - 8 = 13612x−8=136

The equation has exactly one positive root. Locate the root between successive hundredths. x 3 - 3x 2 + 3x - 12 = 0

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Additional Topics in Algebra

Filters

Use synthetic division to find the quotient and the remainder. $\frac { 5 x ^ { 2 } + 2 x - 1 } { x - 1 }$

One root of the equation is given. Determine the remaining roots. $x ^ { 3 } - 9 x ^ { 2 } + 28 x - 40 = 0 ; x = 2 + 2 i$

Find the rational roots and solve the equation. 4x³ - 10x² - 25x + 4 = 0

Determine which of the following real numbers is a root of the equation. $12 x - 8 = 136$

The equation has exactly one positive root. Locate the root between successive hundredths. x³ - 3x² + 3x - 12 = 0