AnswersSummer 2026 Common Core Algebra I - MA3109 B-IC MEF22QXVFactoring Polynomials: Double Grouping

Factoring Polynomials: Double Grouping — Cumulative exam Answers

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1
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Which expression is equivalent to 64y18 – 1000z6?

A
(4y6)3 – (10z2)3
B
(16y6)3 – (10z2)3
C
(16y6)3 – (100z2)3
D
(4y6)3 – (100z2)3
2
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Arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown.162m3n4 + 45n= 9n(_______ + 5)

A
16m3n3
B
16m3n4
C
18m3n3
D
18m3n4
3

Armando used algebra tiles to represent the product .

Question illustration
A
He used the algebra tiles correctly.
B
He did not represent the two original factors correctly.
C
The signs on some of the products are incorrect.
D
Some of the products do not show the correct powers of x.
4

Which is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x – 3

Question illustration
O
Only values that satisfy y > 3x + 1 are solutions.
O
Only values that satisfy y < 3x – 3 are solutions.
V
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
T
There are no solutions.
5

Which describes the range of the parent absolute value function?

A
{y | y is a real number}
B
{y | y is an integer}
C
{y|y > 0}
D
{y|y < 0}
6

An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.)

y
y = 7,746.90(1.02)x
y
y = 7,746.90(0.02)x
y
y = 7,595.96(1.02)x
y
y = 7,595.96(0.02)x
7

Omar grouped the terms and factored the GCF out of the groups of the polynomial 3x3 – 15x2 – 4x + 20. His work is shown.Step 1: (3x3 – 15x2) + (–4x + 20)Step 2: 3x2(x – 5) + 4(–x + 5)

A
Omar should realize that his work shows that the polynomial is prime.
B
Omar should go back and regroup the terms in Step 1 as (3x3 – 15x2) – (4x + 20).
C
In Step 2, Omar should factor only out of the first expression.
D
Omar should factor out a negative from one of the groups so the binomials will be the same.
8

A salad made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3. Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4. Which graph represents the system of equations for this scenario?

Question illustration
A
Option
B
Option
C
Option
D
Option
9

The histogram below shows the number of weeks Jimmy spent different amounts of money to fill the gas tank in his car. If the graph is redrawn so that the scale on the y-axis begins with zero, which aspect of the graph will change the most?

Question illustration
A
The difference in the heights of the bars will not appear as great.
B
The difference in the heights of the bars will be more pronounced.
C
The graph will appear more skewed to the left.
D
The graph will appear more skewed to the right.
10

Which rational expression is undefined when a = 1?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

The system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x.

Question illustration
A
≤
B
≥
C
<
D
>
12

Find the residual values, and use the graphing calculator tool to make a residual plot.

Question illustration
A
Yes, the points have no pattern.
B
No, the points are evenly distributed about the x-axis.
C
No, the points are in a linear pattern.
D
Yes, the points are in a curved pattern.
13

The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a2 + 2. What is X2Y – Z in simplest form?

A
2a2 – 5a – 2
B
3a3 – 6a2 – 2
C
–3a3 – 2
D
–3a2 – 2

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