Given -3i is a root, determine all other roots of f(x) = x3 + 2x2 + 9x + 18.

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

Exam 2: Polynomial and Rational Functions

Find the interval(s) for b such that the following equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients $4 x ^ { 2 } + b x + 13 = 0$ .

(Multiple Choice)

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Question 321

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

(Multiple Choice)

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Question 322

Determine the x-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .

(Multiple Choice)

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Question 323

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

(Multiple Choice)

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Question 324

Write the complex number in standard form. $\sqrt { - 0.0001 }$

(Multiple Choice)

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Question 325

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

(Multiple Choice)

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Question 326

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)

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Question 327

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. 4x⁵ - 8x

(Multiple Choice)

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Question 328

Given -3i is a root, determine all other roots of f(x) = x³ + 2x² + 9x + 18.

(Multiple Choice)

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Question 329

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$ .

(Multiple Choice)

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Question 330

Find two positive real numbers whose product is a maximum. The sum of the first and twice the second is 56. (Round your answer to two decimal places.)

(Multiple Choice)

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Question 331

Use synthetic division to divide. $\frac { x ^ { 3 } + 64 } { x + 4 }$

(Multiple Choice)

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Question 332

Graph the quadratic function. F (x) = - x² - 4x + 1

(Multiple Choice)

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Question 333

Perform the operation and write the result in standard form. $19 i ( 1 - 6 i )$

(Multiple Choice)

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Question 334

Simplify f(x) and find any vertical asymptotes. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$

(Multiple Choice)

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Question 335

Find the interval(s) for b such that the following equation has at least one real solution $x ^ { 2 } + b x + 6 = 0$ .

(Multiple Choice)

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Question 336

An open box is to be made from a square piece of cardboard, 28 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

(Multiple Choice)

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Question 337

Describe the right-hand and the left-hand behavior of the graph of $s ( x ) = 3 x ^ { 5 } + 12 x ^ { 3 } + 3$ .

(Multiple Choice)

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Question 338

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74.

(Multiple Choice)

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Question 339

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )$

(Multiple Choice)

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Question 340

Find the interval(s) for b such that the following equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients $4 x ^ { 2 } + b x + 13 = 0$ .

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

Determine the x-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Write the complex number in standard form. $\sqrt { - 0.0001 }$

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

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.

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. 4x⁵ - 8x

Given -3i is a root, determine all other roots of f(x) = x³ + 2x² + 9x + 18.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$ .

Find two positive real numbers whose product is a maximum. The sum of the first and twice the second is 56. (Round your answer to two decimal places.)

Use synthetic division to divide. $\frac { x ^ { 3 } + 64 } { x + 4 }$

Graph the quadratic function. F (x) = - x² - 4x + 1

Perform the operation and write the result in standard form. $19 i ( 1 - 6 i )$

Simplify f(x) and find any vertical asymptotes. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$

Find the interval(s) for b such that the following equation has at least one real solution $x ^ { 2 } + b x + 6 = 0$ .

An open box is to be made from a square piece of cardboard, 28 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

Describe the right-hand and the left-hand behavior of the graph of $s ( x ) = 3 x ^ { 5 } + 12 x ^ { 3 } + 3$ .

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74.

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )$

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

Exam 2: Polynomial and Rational Functions

Find the interval(s) for b such that the following equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients 4x2+bx+13=04 x ^ { 2 } + b x + 13 = 04x2+bx+13=0 .

Describe the right-hand and the left-hand behavior of the graph of q(x)=−712(x3−x2+2x+1)q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)q(x)=−127​(x3−x2+2x+1) .

Determine the x-intercept(s) of the quadratic function f(x)=x2+2x+2f ( x ) = x ^ { 2 } + 2 x + 2f(x)=x2+2x+2 .

Select the graph of the function y=−6x2y = - 6 x ^ { 2 }y=−6x2 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

Write the complex number in standard form. −0.0001\sqrt { - 0.0001 }−0.0001​

Find the domain of x in the expression 16−x2\sqrt { 16 - x ^ { 2 } }16−x2​ .

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.

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. ​ 4x5 - 8x ​

Given -3i is a root, determine all other roots of f(x) = x3 + 2x2 + 9x + 18.

Determine the zeros (if any) of the rational function f(x)=x2−4x−4f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }f(x)=x−4x2−4​ .

Find two positive real numbers whose product is a maximum. ​ The sum of the first and twice the second is 56. (Round your answer to two decimal places.) ​

Use synthetic division to divide. x3+64x+4\frac { x ^ { 3 } + 64 } { x + 4 }x+4x3+64​

Graph the quadratic function. ​ F (x) = - x2 - 4x + 1 ​

Perform the operation and write the result in standard form. 19i(1−6i)19 i ( 1 - 6 i )19i(1−6i)

Simplify f(x) and find any vertical asymptotes. f(x)=x2−16x+4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }f(x)=x+4x2−16​

Find the interval(s) for b such that the following equation has at least one real solution x2+bx+6=0x ^ { 2 } + b x + 6 = 0x2+bx+6=0 .

An open box is to be made from a square piece of cardboard, 28 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).Determine the function, V, in terms of x, that represents the volume of the box.

Describe the right-hand and the left-hand behavior of the graph of s(x)=3x5+12x3+3s ( x ) = 3 x ^ { 5 } + 12 x ^ { 3 } + 3s(x)=3x5+12x3+3 .

Find the values of b such that the function f(x)=x2+bx−25f ( x ) = x ^ { 2 } + b x - 25f(x)=x2+bx−25 has the given minimum value -74.

Use synthetic division to divide. (3x3−19x2+30x−8)÷(x−4)\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )(3x3−19x2+30x−8)÷(x−4)

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

Find the interval(s) for b such that the following equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients $4 x ^ { 2 } + b x + 13 = 0$ .

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - \frac { 7 } { 12 } \left( x ^ { 3 } - x ^ { 2 } + 2 x + 1 \right)$ .

Determine the x-intercept(s) of the quadratic function $f ( x ) = x ^ { 2 } + 2 x + 2$ .

Select the graph of the function $y = - 6 x ^ { 2 }$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Write the complex number in standard form. $\sqrt { - 0.0001 }$

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

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.

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. 4x⁵ - 8x

Given -3i is a root, determine all other roots of f(x) = x³ + 2x² + 9x + 18.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$ .

Find two positive real numbers whose product is a maximum. The sum of the first and twice the second is 56. (Round your answer to two decimal places.)

Use synthetic division to divide. $\frac { x ^ { 3 } + 64 } { x + 4 }$

Graph the quadratic function. F (x) = - x² - 4x + 1

Perform the operation and write the result in standard form. $19 i ( 1 - 6 i )$

Simplify f(x) and find any vertical asymptotes. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$

Find the interval(s) for b such that the following equation has at least one real solution $x ^ { 2 } + b x + 6 = 0$ .

Describe the right-hand and the left-hand behavior of the graph of $s ( x ) = 3 x ^ { 5 } + 12 x ^ { 3 } + 3$ .

Find the values of b such that the function $f ( x ) = x ^ { 2 } + b x - 25$ has the given minimum value -74.

Use synthetic division to divide. $\left( 3 x ^ { 3 } - 19 x ^ { 2 } + 30 x - 8 \right) \div ( x - 4 )$