Find the value of k such that X - 6 is a factor of x3 - kx2 + 2kx - 24.

A) k = 6 B) k = 10 C) k = 8 D) k = 7 E) k = 9 A) k = 6 B) k = 10 C) k = 8 D) k = 7 E) k = 9

The number (1 + i)is a root of the equation. X 3 - 10x 2 + 18x - 16 = 0 Find the other roots of the equation.

A) x = 1 - i B) x = 1 + i C) x = 5 D) x = 8 A) x = 1 - i B) x = 1 + i C) x = 5 D) x = 8

Exam 13: Polynomial and Synthetic Division

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

(Multiple Choice)

4.9/5

(28)

Question 61

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method. $h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )$

(Multiple Choice)

4.9/5

(31)

Question 62

Find the value of k such that X - 6 is a factor of x³ - kx² + 2kx - 24.

(Multiple Choice)

4.8/5

(26)

Question 63

Use long division to divide. $( 4 x + 2 ) \div ( 2 x + 1 )$

(Multiple Choice)

4.9/5

(35)

Question 64

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )$

(Multiple Choice)

4.8/5

(38)

Question 65

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5$

(Multiple Choice)

4.8/5

(40)

Question 66

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )$

(Multiple Choice)

4.8/5

(41)

Question 67

Using the factors (5x + 4)and (x - 1),find the remaining factor(s)of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.

(Multiple Choice)

4.9/5

(30)

Question 68

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient)+ remainder for the divisor x - 5.

(Multiple Choice)

4.8/5

(38)

Question 69

Use synthetic division to express $P ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 28 x + 63$ in the form (divisor)(quotient)+ remainder for the divisor x + 5.

(Multiple Choice)

4.7/5

(37)

Question 70

Let $P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10$ . Use synthetic division to find the value P (-6).

(Multiple Choice)

4.9/5

(36)

Question 71

Using the factors (x - 4)and (x + 2),find the remaining factor(s)of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.

(Multiple Choice)

4.8/5

(39)

Question 72

Use synthetic division to divide. $\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }$

(Multiple Choice)

4.8/5

(41)

Question 73

The number (1 + i)is a root of the equation. X ³ - 10x ² + 18x - 16 = 0 Find the other roots of the equation.

(Multiple Choice)

4.8/5

(32)

Question 74

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 2 x ^ { 6 } + 8 x ^ { 4 } - 5 x ^ { 2 } + 7 , f ( - 3 )$

(Multiple Choice)

4.8/5

(36)

Question 75

Use Descartes' rule of signs to find the number of possible positive,negative,and nonreal roots for the following equation. 4x ⁷ + 9x ² + 5x + 10 = 0

(Multiple Choice)

4.7/5

(33)

Question 76

Exam 13: Polynomial and Synthetic Division

If x=6x = \sqrt { 6 }x=6​ is a root of x3+5x2−6x−30=0x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0x3+5x2−6x−30=0 ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method.​ h(x)=x3−3x2−6x+5,h(−10)h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )h(x)=x3−3x2−6x+5,h(−10) ​

Find the value of k such that ​ X - 6 is a factor of x3 - kx2 + 2kx - 24. ​

Use long division to divide. ​​ (4x+2)÷(2x+1)( 4 x + 2 ) \div ( 2 x + 1 )(4x+2)÷(2x+1) ​

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ f(x)=3x6−4x4−8x2+3,f(4)f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )f(x)=3x6−4x4−8x2+3,f(4) ​

Select the correct graph of the following function.​ f(x)=6x3+x2−9x+5f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5f(x)=6x3+x2−9x+5

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ h(x)=x3−4x2−9x+7,h(2)h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )h(x)=x3−4x2−9x+7,h(2) ​

Using the factors (5x + 4)and (x - 1),find the remaining factor(s)of f(x)=−20x4+109x3−30x2−79x+20f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20f(x)=−20x4+109x3−30x2−79x+20 and write the polynomial in fully factored form.

Use synthetic division to express P(x)=3x3−10x2−23x−35P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35P(x)=3x3−10x2−23x−35 in the form (divisor)(quotient)+ remainder for the divisor x - 5. ​

Use synthetic division to express P(x)=2x3+3x2−28x+63P ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 28 x + 63P(x)=2x3+3x2−28x+63 in the form (divisor)(quotient)+ remainder for the divisor x + 5. ​

Let P(x)=7x3+4x2−9x+10P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10P(x)=7x3+4x2−9x+10 . ​ Use synthetic division to find the value P (-6). ​

Using the factors (x - 4)and (x + 2),find the remaining factor(s)of f(x)=x3+x2−14x−24f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24f(x)=x3+x2−14x−24 and write the polynomial in fully factored form.

Use synthetic division to divide. −4x3+23x2−31x+124x−3\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }4x−3−4x3+23x2−31x+12​

The number (1 + i)is a root of the equation. ​ X 3 - 10x 2 + 18x - 16 = 0 ​ Find the other roots of the equation. ​

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.​ f(x)=2x6+8x4−5x2+7,f(−3)f ( x ) = 2 x ^ { 6 } + 8 x ^ { 4 } - 5 x ^ { 2 } + 7 , f ( - 3 )f(x)=2x6+8x4−5x2+7,f(−3) ​

Use Descartes' rule of signs to find the number of possible positive,negative,and nonreal roots for the following equation. 4x 7 + 9x 2 + 5x + 10 = 0

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ ,use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Use the Remainder Theorem and synthetic division to find each function value.Verify your answers using another method. $h ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 6 x + 5 , h ( - 10 )$

Find the value of k such that X - 6 is a factor of x³ - kx² + 2kx - 24.

Use long division to divide. $( 4 x + 2 ) \div ( 2 x + 1 )$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 3 x ^ { 6 } - 4 x ^ { 4 } - 8 x ^ { 2 } + 3 , f ( 4 )$

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )$

Using the factors (5x + 4)and (x - 1),find the remaining factor(s)of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.

Use synthetic division to express $P ( x ) = 3 x ^ { 3 } - 10 x ^ { 2 } - 23 x - 35$ in the form (divisor)(quotient)+ remainder for the divisor x - 5.

Use synthetic division to express $P ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 28 x + 63$ in the form (divisor)(quotient)+ remainder for the divisor x + 5.

Let $P ( x ) = 7 x ^ { 3 } + 4 x ^ { 2 } - 9 x + 10$ . Use synthetic division to find the value P (-6).

Using the factors (x - 4)and (x + 2),find the remaining factor(s)of $f ( x ) = x ^ { 3 } + x ^ { 2 } - 14 x - 24$ and write the polynomial in fully factored form.

Use synthetic division to divide. $\frac { - 4 x ^ { 3 } + 23 x ^ { 2 } - 31 x + 12 } { 4 x - 3 }$

The number (1 + i)is a root of the equation. X ³ - 10x ² + 18x - 16 = 0 Find the other roots of the equation.

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 2 x ^ { 6 } + 8 x ^ { 4 } - 5 x ^ { 2 } + 7 , f ( - 3 )$

Use Descartes' rule of signs to find the number of possible positive,negative,and nonreal roots for the following equation. 4x ⁷ + 9x ² + 5x + 10 = 0