Find all the zeros of the function. X3 + 7x2 + 32x + 60

A) -4, -3 ± 2i B) -3, -2 ± 4i C) -3, 2 ± 4i D) -3, 2 ± i E) -3, -4 ± 2i A) -4, -3 ± 2i B) -3, -2 ± 4i C) -3, 2 ± 4i D) -3, 2 ± i E) -3, -4 ± 2i

Write the polynomial in completely factored form. F(x) = x4 + 20x2 - 125

A) $( x + 5 ) ( x - 5 ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } )$ B) $( x + 5 ) ( x - 5 i ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } i )$ C) $( x + 5 ) ( x - 5 ) ( x + \sqrt { 5 } i ) ( x - \sqrt { 5 } i )$ D) $( x + 5 i ) ( x - 5 i ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } )$ E) $( x + 5 i ) ( x - 5 ) ( x + \sqrt { 5 i } ) ( x - \sqrt { 5 } )$ A) $( x + 5 ) ( x - 5 ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } )$ B) $( x + 5 ) ( x - 5 i ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } i )$ C) $( x + 5 ) ( x - 5 ) ( x + \sqrt { 5 } i ) ( x - \sqrt { 5 } i )$ D) $( x + 5 i ) ( x - 5 i ) ( x + \sqrt { 5 } ) ( x - \sqrt { 5 } )$ E) $( x + 5 i ) ( x - 5 ) ( x + \sqrt { 5 i } ) ( x - \sqrt { 5 } )$

Exam 2: Polynomial and Rational Functions

Using the factors (x - 5) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 30$ and write the polynomial in fully factored form.

(Multiple Choice)

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Question 421

Find the domain of the function $f ( x ) = \frac { 9 } { x - 8 }$ .

(Multiple Choice)

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Question 422

Use long division to divide. $\left( x ^ { 4 } + 4 x ^ { 2 } + 6 \right) \div \left( x ^ { 2 } + x + 4 \right)$

(Multiple Choice)

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Question 423

Find the zeros (if any) of the rational function. $f ( x ) = 1 - \frac { 8 } { x - 8 }$

(Multiple Choice)

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Question 424

Find all intercepts of the following function. $f ( t ) = \frac { 1 - 8 t } { t }$

(Multiple Choice)

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Question 425

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$ and determine the multiplicity of each.

(Multiple Choice)

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Question 426

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 4$ .

(Multiple Choice)

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Question 427

Simplify the rational expression, $\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }$ , by using long division or synthetic division.

(Multiple Choice)

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Question 428

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function. $h ( t ) = t ^ { 2 } - 14 t + 49$

(Multiple Choice)

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Question 429

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }$

(Multiple Choice)

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Question 430

Use long division to divide. $\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )$

(Multiple Choice)

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Question 431

Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } > 0$

(Multiple Choice)

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Question 432

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .

(Multiple Choice)

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Question 433

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

(Multiple Choice)

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Question 434

Write the number of rational and irrational zeros of the given cubic function. X³ - 2

(Multiple Choice)

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Question 435

Perform the operation and write the result in standard form. $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$

(Multiple Choice)

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Question 436

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

(Multiple Choice)

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Question 437

Find all the zeros of the function. X³ + 7x² + 32x + 60

(Multiple Choice)

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Question 438

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$ .

(Multiple Choice)

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Question 439

Write the polynomial in completely factored form. F(x) = x⁴ + 20x² - 125

(Multiple Choice)

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Question 440

Using the factors (x - 5) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 30$ and write the polynomial in fully factored form.

Find the domain of the function $f ( x ) = \frac { 9 } { x - 8 }$ .

Use long division to divide. $\left( x ^ { 4 } + 4 x ^ { 2 } + 6 \right) \div \left( x ^ { 2 } + x + 4 \right)$

Find the zeros (if any) of the rational function. $f ( x ) = 1 - \frac { 8 } { x - 8 }$

Find all intercepts of the following function. $f ( t ) = \frac { 1 - 8 t } { t }$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$ and determine the multiplicity of each.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 4$ .

Simplify the rational expression, $\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }$ , by using long division or synthetic division.

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function. $h ( t ) = t ^ { 2 } - 14 t + 49$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }$

Use long division to divide. $\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )$

Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } > 0$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .

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

Write the number of rational and irrational zeros of the given cubic function. X³ - 2

Perform the operation and write the result in standard form. $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Find all the zeros of the function. X³ + 7x² + 32x + 60

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$ .

Write the polynomial in completely factored form. F(x) = x⁴ + 20x² - 125

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

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Exam 2: Polynomial and Rational Functions

Using the factors (x - 5) and (x + 2), find the remaining factor(s) of f(x)=x3−6x2−x+30f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 30f(x)=x3−6x2−x+30 and write the polynomial in fully factored form.

Find the domain of the function f(x)=9x−8f ( x ) = \frac { 9 } { x - 8 }f(x)=x−89​ .

Use long division to divide. (x4+4x2+6)÷(x2+x+4)\left( x ^ { 4 } + 4 x ^ { 2 } + 6 \right) \div \left( x ^ { 2 } + x + 4 \right)(x4+4x2+6)÷(x2+x+4)

Find the zeros (if any) of the rational function. f(x)=1−8x−8f ( x ) = 1 - \frac { 8 } { x - 8 }f(x)=1−x−88​

Find all intercepts of the following function. f(t)=1−8ttf ( t ) = \frac { 1 - 8 t } { t }f(t)=t1−8t​

Find all real zeros of the polynomial f(x)=x3+5x2−4x−20f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20f(x)=x3+5x2−4x−20 and determine the multiplicity of each.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x)=2x3−2x2+3x−4f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 4f(x)=2x3−2x2+3x−4 .

Simplify the rational expression, x4+3x3−25x2−39x+180x2−6x+9\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }x2−6x+9x4+3x3−25x2−39x+180​ , by using long division or synthetic division.

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function. h(t)=t2−14t+49h ( t ) = t ^ { 2 } - 14 t + 49h(t)=t2−14t+49

Find the domain of the function and identify any vertical and horizontal asymptotes. f(x)=2x2x+3f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }f(x)=x+32x2​

Use long division to divide. (−x2−5x−6)÷(x+2)\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )(−x2−5x−6)÷(x+2)

Solve the inequality and write the solution set in interval notation. 5x3−20x2>05 x ^ { 3 } - 20 x ^ { 2 } > 05x3−20x2>0

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=1x−5f ( x ) = \frac { 1 } { x - 5 }f(x)=x−51​ .

Use the Remainder Theorem and synthetic division to find the function value.Verify your answers using another method. h(x)=x3−2x2−5x+6,h(−8)h ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 5 x + 6 , \quad h ( - 8 )h(x)=x3−2x2−5x+6,h(−8)

Write the number of rational and irrational zeros of the given cubic function. ​ X3 - 2 ​

Perform the operation and write the result in standard form. (19+8i)(19−8i)( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )(19​+8​i)(19​−8​i)

Select the graph of the function y=(x−4)2+1y = ( x - 4 ) ^ { 2 } + 1y=(x−4)2+1 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Find all the zeros of the function. ​ X3 + 7x2 + 32x + 60 ​

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x)=4x3+3x2+5x+1f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1f(x)=4x3+3x2+5x+1 .

Write the polynomial in completely factored form. F(x) = x4 + 20x2 - 125

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Using the factors (x - 5) and (x + 2), find the remaining factor(s) of $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - x + 30$ and write the polynomial in fully factored form.

Find the domain of the function $f ( x ) = \frac { 9 } { x - 8 }$ .

Use long division to divide. $\left( x ^ { 4 } + 4 x ^ { 2 } + 6 \right) \div \left( x ^ { 2 } + x + 4 \right)$

Find the zeros (if any) of the rational function. $f ( x ) = 1 - \frac { 8 } { x - 8 }$

Find all intercepts of the following function. $f ( t ) = \frac { 1 - 8 t } { t }$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20$ and determine the multiplicity of each.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 4$ .

Simplify the rational expression, $\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }$ , by using long division or synthetic division.

Find all the real zeros of the polynomial function and determine the multiplicity of each zero and the number of turning points of the graph of the function. $h ( t ) = t ^ { 2 } - 14 t + 49$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }$

Use long division to divide. $\left( - x ^ { 2 } - 5 x - 6 \right) \div ( x + 2 )$

Solve the inequality and write the solution set in interval notation. $5 x ^ { 3 } - 20 x ^ { 2 } > 0$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .

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

Write the number of rational and irrational zeros of the given cubic function. X³ - 2

Perform the operation and write the result in standard form. $( \sqrt { 19 } + \sqrt { 8 } i ) ( \sqrt { 19 } - \sqrt { 8 } i )$

Select the graph of the function $y = ( x - 4 ) ^ { 2 } + 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Find all the zeros of the function. X³ + 7x² + 32x + 60

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$ .

Write the polynomial in completely factored form. F(x) = x⁴ + 20x² - 125