Polynomial functions

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ALBerTA DISTANCe LeArNING CeNTre MAT3791

Math 30-1 Unit 1: Functions

Lesson B: Polynomial Functions

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NEW October 2012

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Summary

Total Weighting

your Marks

Practice Self- Assessment 20%

Assignment 80%

Blended Booklet Grade

Alberta Distance Learning Centre 107

Mathematics 30-1: Unit 1 Lesson B - Assignment Booklet

Back to Baker Street… Complete the Back to Baker Street assignment. Refer to the Tips from Scotland Yard located at the back of this lesson booklet to assist you in completing the assignment. Please show pertinent work and explanation.

Call or e-mail your teacher if you would like additional help.

Multiple-Choice Items

_________ 1. Select the correct chart for the polynomial function f(x) = 4x2+ 8x3 + 2x – 6.

A. Degree Leading Coefficient

Constant Term

5 2 –6

B. Degree Leading Coefficient

Constant Term

2 4 –6

C. Degree Leading Coefficient

Constant Term

6 –6 4

D. Degree Leading Coefficient

Constant Term

3 8 –6

_________ 2. For the polynomial function g(x) = ax4 + bx3 + 6x, the y-intercept and the maximum number of possible x-intercepts are

A. 0 and 4 B. 0 and 7 C 6 and 6 D. 6 and 3

_________ 3. The possible integral zeros of f(x) = 4x3 + 5x2 + 7x + 6

A. ±1, ±2, ±4 B. ±1, ±2, ±3, ±6 C. ±1 ±7 D. ±1, ±5

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108 Alberta Distance Learning Centre

Lesson B - Assignment Booklet Mathematics 30-1: Unit 1

_________ 4. Which binomial is a factor of the polynomial x3– 7x + 6?

A. x + 3 B. x – 6 C. x – 3 D. x + 2

Numeric Response 1

Given that the volume of a rectangular box is modelled by the polynomial V(x) = x3 – 15x2 + 71x, and the volume is 105 cubic units. Give the possible values of x in ascending order.

_________ 5. The remainder when 2x3 + 4x – 5 is divided by x + 2 is

A. 19 B. –29 C. –5 D. 11

_________ 6. The multiplicity of 2 in the function f(x) = x2(x + 2)3(x – 2) is

A. 1 B. 2 C. 3 D. 0

_________ 7. The interval where f(x) = –2(x + 2)(x – 3)(x – 1) is positive will be

A. x > 0 B. –2 < x < 1, x > 3 C. x < –2, 1 < x < 3 D. x < 0

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Alberta Distance Learning Centre 109

Mathematics 30-1: Unit 1 Lesson B - Assignment Booklet

Numeric Response 2

Determine the value of k in f(x) = 5x3 + kx2 – 4x + 4 so that x + 2 is a factor.

_________ 8. The statement that best describes the end behaviour of g(x) = 2x(x + 3)(x – 2)(x + 1) is

A. extends upward into Quadrant I and upward into Quadrant II B. extends downward into Quadrant IV and downward into Quadrant III C. extends upward into Quadrant I and downward into Quadrant III D. extends downward into Quadrant IV and upward into Quadrant II

_________ 9. Determine the value of Q(x) when P(x) = 4x3 – 3x2 + 2x + 5 is divided by x – 3

and is then expressed in the form ( ) ( )

( ) x P x

Q x x R

3 3- = + -^ h

.

A. 4x2 – 15x + 47 B. 4x3 – 3x2 + 2x + 5 C. 4x2 – 15x – 43 D. 4x2 + 9x + 29

Written Response

1. Factor fully the polynomial 2x4 – 3x3 – 17x2 + 30x. Show all your work. (L)

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110 Alberta Distance Learning Centre

Lesson B - Assignment Booklet Mathematics 30-1: Unit 1

2. When a type of plastic pipe is cut into sections, the length of each section determines its relative strength.

The function f(x) = x4 – 6x3 – 22x2 + 95x + 100 describes the relative strength of a section with length x feet.

After testing the plastic, engineers discovered that 4 ft sections were extremely weak.

a. Graph the function showing zeros of the polynomial. (O)

b. Define where the function is positive and where it is negative. (O)

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2

Alberta Distance Learning Centre 111

Mathematics 30-1: Unit 1 Lesson B - Assignment Booklet

c. Describe what the integral zeros represent in terms of this specific situation. (O)

d. Given the strength of pipe is 20 units, determine the corresponding length(s) of pipe rounded to two decimal places. (S)

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112 Alberta Distance Learning Centre

Lesson B - Assignment Booklet Mathematics 30-1: Unit 1

S Standard of Excellence • Students need to make connections to other courses to complete. • Successful completion shows an ability to think beyond given examples.

O

Over the acceptable level of understanding • Students need to make connections from within the course notes and

example to complete. • Successful completion shows an ability to draw from given instruction and

apply skills to new problems.

L Level of acceptable standards • Students need to show an acceptable level of understanding to complete. • Successful completion shows an ability follow given examples.

V Below level of acceptable standards • Student's response to question is below acceptable standard.

E Inadequate level of acceptable standards • Student's response to question indicates student needs assistance in

understanding basic concepts.

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