Question 1

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X3 - 6x2 + x + 164
​
​

Accepted Answer

A) -4,5 ± 4i; (x + 4)(x - 5 + 4i)(x - 5 - 4i) 
B) -4,5 ± 4i; (x + 4)(x - 5 + 4i)(x + 5 - 4i) 
C) 4,5 ± 4i; (x - 4)(x - 5 + 4i)(x - 5 - 4i) 
D) -4,5 ± 4i; (x + 4)(x + 5 + 4i)(x + 5 - 4i) 
E) -4,5 ± 4i; (x + 4)(x - 5 - 4i)(x - 5 - 4i) 
A) -4,5 ± 4i; (x + 4)(x - 5 + 4i)(x - 5 - 4i) 
B) -4,5 ± 4i; (x + 4)(x - 5 + 4i)(x + 5 - 4i) 
C) 4,5 ± 4i; (x - 4)(x - 5 + 4i)(x - 5 - 4i) 
D) -4,5 ± 4i; (x + 4)(x + 5 + 4i)(x + 5 - 4i) 
E) -4,5 ± 4i; (x + 4)(x - 5 - 4i)(x - 5 - 4i) A

Question 2

Find a polynomial function with real coefficients that has the given zeros. ​
6,-6i
​

Accepted Answer

A) x3 - 6x2 - 36x - 216 
B) x3 - 6x2 + 36x + 216 
C) x3 + 6x2 + 36x + 216 
D) x3 - 6x2 + 36x - 216 
E) x3 + 6x2 + 36x - 216 
A) x3 - 6x2 - 36x - 216 
B) x3 - 6x2 + 36x + 216 
C) x3 + 6x2 + 36x + 216 
D) x3 - 6x2 + 36x - 216 
E) x3 + 6x2 + 36x - 216 D

Question 3

Use the given zero to find all the zeros of the function. ​
Function Zero
X3 - 3x2 + 16x - 48 4i
​

Accepted Answer

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

Question 4

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section)of 168 inches.​   ​ Write a function that represents the volume of the package.
​

Accepted Answer

A) V(x)= - 4x2(42 + x) 
B) V(x)= 4x2(42 + x) 
C) V(x)= 4x2(42 - x) 
D) V(x)= 4x2(-42 - x) 
E) V(x)= - 4x2(42 - x) 
A) V(x)= - 4x2(42 + x) 
B) V(x)= 4x2(42 + x) 
C) V(x)= 4x2(42 - x) 
D) V(x)= 4x2(-42 - x) 
E) V(x)= - 4x2(42 - x)

Question 5

Find a polynomial function with real coefficients that has the given zeros. ​
2,4 + 3i
​

Accepted Answer

A) x3 - 10x2 + 41x + 50 
B) x3 + 10x2 + 41x + 50 
C) x3 - 10x2 + 41x - 50 
D) x3 - 10x2 - 41x - 50 
E) x3 + 10x2 + 41x - 50 
A) x3 - 10x2 + 41x + 50 
B) x3 + 10x2 + 41x + 50 
C) x3 - 10x2 + 41x - 50 
D) x3 - 10x2 - 41x - 50 
E) x3 + 10x2 + 41x - 50

Question 6

Find all the zeros of the function. ​
X(x - 5)2
​

Accepted Answer

A) 0,5 
B) 1,5 
C) ±5 
D) 1,-5 
E) 0,-5 
A) 0,5 
B) 1,5 
C) ±5 
D) 1,-5 
E) 0,-5

Question 7

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x)= x6 - 9x4 + 11x2 + 21 accurate to the nearest thousandth.

Accepted Answer

A) 2.646,1.732 
B) ±1,-2.646,1.732 
C) ±i,-2.646,-1.732 
D) ±1,2.646,1.732 
E) ±i,±2.646,±1.732 
A) 2.646,1.732 
B) ±1,-2.646,1.732 
C) ±i,-2.646,-1.732 
D) ±1,2.646,1.732 
E) ±i,±2.646,±1.732

Question 8

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
Y4 - 2401
​

Accepted Answer

A) ±7; (y - 7)(y + 7) 
B) ±7,±7i; (y - 7)(y + 7)(y - 7i)(y + 7i) 
C) 7,7i; (y + 7)(y + 7)(y - 7i)(y - 7i) 
D) ±7i; (y - 7i)(y + 7i) 
E) ±7,±7i; (y - 7)(y - 7)(y + 7i)(y + 7i) 
A) ±7; (y - 7)(y + 7) 
B) ±7,±7i; (y - 7)(y + 7)(y - 7i)(y + 7i) 
C) 7,7i; (y + 7)(y + 7)(y - 7i)(y - 7i) 
D) ±7i; (y - 7i)(y + 7i) 
E) ±7,±7i; (y - 7)(y - 7)(y + 7i)(y + 7i)

Question 9

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x)= 6x3 + 3x2 + 3x + 4.

Accepted Answer

A) no positive reals;no negative reals 
B) 1 positive real;3 negative reals or 1 negative real 
C) 0 positive real;3 negative reals or 1 negative real 
D) 3 positive reals or 1 positive real;no negative reals 
E) 3 positive reals or 1 positive real;3 negative reals or 1 negative real 
A) no positive reals;no negative reals 
B) 1 positive real;3 negative reals or 1 negative real 
C) 0 positive real;3 negative reals or 1 negative real 
D) 3 positive reals or 1 positive real;no negative reals 
E) 3 positive reals or 1 positive real;3 negative reals or 1 negative real

Question 10

Find all the rational zeros of the function f(x)= 2x5 - 9x4 + 9x3 - 3x2 + 7x + 6.

Accepted Answer

A) x = $- \frac { 1 } { 2 }$ ,3,2 
B) x = $- \frac { 2 } { 3 }$ ,-1,2 
C) x = $\frac { 1 } { 2 }$ ,3,1 
D) x = $- \frac { 1 } { 2 }$ , $\frac { 3 } { 2 }$ 
E) x = $- \frac { 1 } { 2 }$ , $\frac { 3 } { 2 }$ ,2 
A) x = $- \frac { 1 } { 2 }$ ,3,2 
B) x = $- \frac { 2 } { 3 }$ ,-1,2 
C) x = $\frac { 1 } { 2 }$ ,3,1 
D) x = $- \frac { 1 } { 2 }$ , $\frac { 3 } { 2 }$ 
E) x = $- \frac { 1 } { 2 }$ , $\frac { 3 } { 2 }$ ,2

Question 11

Find all the real zeros of f(x)= 3x3 - 9x2 + 3x - 9.

Accepted Answer

A) x = 3 
B) x = 3, $- \frac { 1 } { 3 }$ 
C) x = $\frac { 1 } { 3 }$ , $- \frac { 1 } { 9 }$ 
D) x = ±1,3 
E) x = 3,1,-9 
A) x = 3 
B) x = 3, $- \frac { 1 } { 3 }$ 
C) x = $\frac { 1 } { 3 }$ , $- \frac { 1 } { 9 }$ 
D) x = ±1,3 
E) x = 3,1,-9

Question 12

Find all the zeros of the function. ​
(t - 4)(t - 3)(t - 6i)(t + 6i)
​

Accepted Answer

A) -4,-3,±6i 
B) 4,3,6i 
C) 4,3,±6i 
D) -4,3,±6i 
E) 4,-3,±6i 
A) -4,-3,±6i 
B) 4,3,6i 
C) 4,3,±6i 
D) -4,3,±6i 
E) 4,-3,±6i

Question 13

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X3 - 10x2 + 29x - 30
​

Accepted Answer

A) 2 ± i;6; (x - 2 + i)(x + 2 - i)(x - 6) 
B) 2 ± i;6; (x - 2 + i)(x - 2 + i)(x - 6) 
C) -2 ± i;6; (x + 2 + i)(x + 2 - i)(x - 6) 
D) 2 ± i;-6; (x - 2 + i)(x - 2 - i)(x + 6) 
E) 2 ± i;6; (x - 2 + i)(x - 2 - i)(x - 6) 
A) 2 ± i;6; (x - 2 + i)(x + 2 - i)(x - 6) 
B) 2 ± i;6; (x - 2 + i)(x - 2 + i)(x - 6) 
C) -2 ± i;6; (x + 2 + i)(x + 2 - i)(x - 6) 
D) 2 ± i;-6; (x - 2 + i)(x - 2 - i)(x + 6) 
E) 2 ± i;6; (x - 2 + i)(x - 2 - i)(x - 6)

Question 14

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. ?
F(x)= x4 + 42x2 - 343
?

Accepted Answer

A)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )$ 
B)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x + \sqrt { 7 } )$ 
C)  $\left( x ^ { 2 } + 49 \right) ( x - \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
D)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
E)  $\left( x ^ { 2 } + 49 \right) ( x + 7 ) ( x - \sqrt { 7 } )$ 
A)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )$ 
B)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x + \sqrt { 7 } )$ 
C)  $\left( x ^ { 2 } + 49 \right) ( x - \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
D)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
E)  $\left( x ^ { 2 } + 49 \right) ( x + 7 ) ( x - \sqrt { 7 } )$

Question 15

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

Accepted Answer

A) One negative zero 
B) One negative zero or three positive zeros 
C) Two negative zeros or no positive zero 
D) One positive zero,one negative zero 
E) One negative zero,four negative zeros 
A) One negative zero 
B) One negative zero or three positive zeros 
C) Two negative zeros or no positive zero 
D) One positive zero,one negative zero 
E) One negative zero,four negative zeros

Question 16

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

Accepted Answer

A) Rational zeros: 1;irrational zeros: 0 
B) Rational zeros: 1;irrational zeros: 2 
C) Rational zeros: 1;irrational zeros: 1 
D) Rational zeros: 0;irrational zeros: 1 
E) Rational zeros: 0;irrational zeros: 0 
A) Rational zeros: 1;irrational zeros: 0 
B) Rational zeros: 1;irrational zeros: 2 
C) Rational zeros: 1;irrational zeros: 1 
D) Rational zeros: 0;irrational zeros: 1 
E) Rational zeros: 0;irrational zeros: 0

Question 17

Find all zeros of the function f(x)= (x - 4)(x + 4i)(x - 4i).

Accepted Answer

A) x = 4,-4i,4i 
B) x = 4 
C) x = 4,4i 
D) x = 4,-4,4 
E) x = -4,-4i,4i 
A) x = 4,-4i,4i 
B) x = 4 
C) x = 4,4i 
D) x = 4,-4,4 
E) x = -4,-4i,4i

Question 18

Find a polynomial with real coefficients that has zeros -1,3i,and -3i.

Accepted Answer

A) x3 + 9x2 + x + 9 
B) x3 + x2 - 9x - 9 
C) x3 + x2 + 3x + 3 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x - 9 
A) x3 + 9x2 + x + 9 
B) x3 + x2 - 9x - 9 
C) x3 + x2 + 3x + 3 
D) x3 + x2 + 9x + 9 
E) x3 - x2 + 9x - 9

Question 19

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
X4 - 81
​

Accepted Answer

A) 3,3i; (x + 3)(x + 3)(x - 3i)(x - 3i) 
B) ±3i; (x - 3i)(x + 3i) 
C) ±3,±3i; (x - 3)(x - 3)(x + 3i)(x + 3i) 
D) ±3; (x - 3)(x + 3) 
E) ±3,±3i; (x - 3)(x + 3)(x - 3i)(x + 3i) 
A) 3,3i; (x + 3)(x + 3)(x - 3i)(x - 3i) 
B) ±3i; (x - 3i)(x + 3i) 
C) ±3,±3i; (x - 3)(x - 3)(x + 3i)(x + 3i) 
D) ±3; (x - 3)(x + 3) 
E) ±3,±3i; (x - 3)(x + 3)(x - 3i)(x + 3i)

Question 20

Find a polynomial with the given zeros.? $i , \sqrt { 7 } , - i$ ?

Accepted Answer

A) ? $x ^ { 3 } - 7 x$ 
B)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$ 
C)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + x - 7$ 
E) none of these 
A) ? $x ^ { 3 } - 7 x$ 
B)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + x - \sqrt { 7 }$ 
C)  $x ^ { 3 } - \sqrt { 7 } x ^ { 2 } + 7 x - \sqrt { 7 }$ 
D)  $x ^ { 3 } - 7 x ^ { 2 } + x - 7$ 
E) none of these

Exam 15: Zeros of Polynomial Functions

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X3 - 6x2 + x + 164 ​ ​

Find a polynomial function with real coefficients that has the given zeros. ​ 6,-6i ​

Use the given zero to find all the zeros of the function. ​ Function Zero X3 - 3x2 + 16x - 48 4i ​

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section)of 168 inches.​ ​ Write a function that represents the volume of the package. ​

Find a polynomial function with real coefficients that has the given zeros. ​ 2,4 + 3i ​

Find all the zeros of the function. ​ X(x - 5)2 ​

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x)= x6 - 9x4 + 11x2 + 21 accurate to the nearest thousandth.

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ Y4 - 2401 ​

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x)= 6x3 + 3x2 + 3x + 4.

Find all the rational zeros of the function f(x)= 2x5 - 9x4 + 9x3 - 3x2 + 7x + 6.

Find all the real zeros of f(x)= 3x3 - 9x2 + 3x - 9.

Find all the zeros of the function. ​ (t - 4)(t - 3)(t - 6i)(t + 6i) ​

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X3 - 10x2 + 29x - 30 ​

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. ? F(x)= x4 + 42x2 - 343 ?

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

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

Find all zeros of the function f(x)= (x - 4)(x + 4i)(x - 4i).

Find a polynomial with real coefficients that has zeros -1,3i,and -3i.

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ X4 - 81 ​

Find a polynomial with the given zeros.? i,7,−ii , \sqrt { 7 } , - ii,7​,−i ?

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

Polynomial and Synthetic Division

Complex Numbers

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

Find all the zeros of the function and write the polynomial as a product of linear factors. X³ - 6x² + x + 164

Find a polynomial function with real coefficients that has the given zeros. 6,-6i

Use the given zero to find all the zeros of the function. Function Zero X³ - 3x² + 16x - 48 4i

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section)of 168 inches. Write a function that represents the volume of the package.

Find a polynomial function with real coefficients that has the given zeros. 2,4 + 3i

Find all the zeros of the function. X(x - 5)²

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x)= x⁶ - 9x⁴ + 11x² + 21 accurate to the nearest thousandth.

Find all the zeros of the function and write the polynomial as a product of linear factors. Y⁴ - 2401

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f(x)= 6x³ + 3x² + 3x + 4.

Find all the rational zeros of the function f(x)= 2x⁵ - 9x⁴ + 9x³ - 3x² + 7x + 6.

Find all the real zeros of f(x)= 3x³ - 9x² + 3x - 9.

Find all the zeros of the function. (t - 4)(t - 3)(t - 6i)(t + 6i)

Find all the zeros of the function and write the polynomial as a product of linear factors. X³ - 10x² + 29x - 30

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. ? F(x)= x⁴ + 42x² - 343 ?

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

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

Find all the zeros of the function and write the polynomial as a product of linear factors. X⁴ - 81

Find a polynomial with the given zeros.? $i , \sqrt { 7 } , - i$ ?