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Embedded Assessment 3
Polynomial Operations
Embedded Assessment 3
MEASURING UP
Use after Activity 25
1. The missing side has area
4x2 − x + 3. The surface area is
2(x2 + 2x + 1) + 2(4x2 + 5x + 7) +
2(missing area) = 18x2 + 12x + 22.
First, multiply 2(x2 + 2x + 1) and
2(4x2 + 5x + 7) by using the
Distributive Property. Then, add the
two resulting polynomials and
subtract the sum from 18x2 + 12x +
22 to get 8x2 − 2x + 6 = 2(missing
area). Therefore, the missing area is
4x2 − x + 3.
2. Explanations may vary. The volume
is calculated incorrectly. The surface
area is correct.
V = 2x(x + 3)(x + 12)
= 2x(x2 + 15x + 36)
= 2x3 + 30x2 + 72x
SA = 2(2x)(x + 3) + 2(2x)(x + 12) +
2(x + 3)(x + 12)
= 4x2 + 12x + 4x2 + 48x +
2x2 + 30x + 72
= 10x2 + 90x + 72
3. The volume is 18πx5y3.
V = πr2h
V = π(3x2y)2(2xy)
V = π(3x2y)(3x2y)(2xy)
V = 18πx5y3
x2 + 2x + 1
4x2 + 5x + 7
?
The formula for the volume of a rectangular prism
is V = lwh, where l, w, and h are length, width, and height, respectively. The
formula for the surface area is SA = 2lw + 2wh + 2lh.
2. Complete the second part of the job application by verifying whether or
not the following computations are
correct. Explain your reasoning by
2x
showing your work.
Volume:
2x2 + 15x + 36
Surface Area:
10x2 + 90x + 72
x+3
x + 12
© 2014 College Board. All rights reserved.
3. Complete the final part of the job application by writing an expression
for the volume of a cylinder with radius 3x2y and height 2xy. Use the
formula V = πr2h where r is the radius and h is the height. Simplify
your answer as much as possible.
© 2014 College Board. All rights reserved.
• Adding polynomials
• Multiplying polynomials
Answer Key
Employees at Ship-It-Quik must perform computations involving volume
and surface area. As part of the job application, potential employees must
take a test that involves surface area, volume, and algebraic skills.
1. The surface area of a figure is the total area of
all faces. The areas of the faces of a rectangular
prism are shown. The surface area of this
prism is 18x2 + 12x + 22. Complete the first
part of the job application by finding the area
of the missing face.
Assessment Focus
Unit 4 • Exponents, Radicals, and Polynomials
383
Common Core State Standards for Embedded Assessment 3
HSA-APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are
closed under the operations of addition, subtraction, and multiplication; add, subtract,
and multiply polynomials.
Unit 4 • Exponents, Radicals, and Polynomials
383