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

Factoring Polynomials: Double Grouping — Cumulative exam Answers

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The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

A
(–∞, –7)
B
(–∞, –1)
C
(–∞, 1)
D
(–∞, 7)
2
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Which equation represents the function f(x) = (1.6)x after it has been translated 5 units up and 9 units to the right?

A
g(x) = (1.6)x + 5 − 9
B
g(x) = (1.6)x + 5 + 9
C
g(x) = (1.6)x − 9 + 5
D
g(x) = (1.6)x + 9 + 5
3

The number of bacteria in a sample after x days is represented using the equation . By what approximate percent does the population change per day?

Question illustration
A
4.8% decrease
B
5.0% increase
C
95.2% decrease
D
105.0% increase
4

Teresa is factoring this polynomial by grouping. Which common factors should be used in the next step of factoring?10x3+3x2−20x−6(10x3+3x2)+(−20x−6)

A
x2 and −2x
B
2x2 and −2x
C
x2 and −2
D
2x2 and −2
5

The formula for the area of a triangle is , where b is the length of the base and h is the height.Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

Question illustration
A
3 units
B
5 units
C
8 units
D
9 units
6

Which statement is true about the function f(x) = ?

Question illustration
A
It has the same domain as the function f(x) = .
Option A
B
It has the same range as the function f(x) = .
Option B
C
It has the same domain as the function f(x) = .
Option C
D
It has the same range as the function f(x) = .
Option D
7

What is the rate of increase for the function f(x) = ?

Question illustration
A
One-third
Option A
B
2
Option B
C
4
D
4
Option D
8

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
9

Which is equivalent to ?

Question illustration
A
3
B
6
C
9
D
12
10

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.
11

A biologist begins working with a sample containing 20,000 bacteria. The population size doubles every 10 days according to the equation , where t represents the number of days. After seven days the biologist begins working with a second sample of 20,000 bacteria. The equation used to represent the population of sample 2 after t days is . Which of the following is an equivalent form of the equation for the population of sample 2?

Question illustration
A
mc006-3.jpg
Option A
B
mc006-4.jpg
Option B
C
mc006-5.jpg
Option C
D
mc006-6.jpg
Option D
12

Consider the expression . Which of the following is an equivalent expression?

Question illustration
A
mc002-2.jpg
Option A
B
mc002-3.jpg
Option B
C
mc002-4.jpg
Option C
D
mc002-5.jpg
Option D
13

Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function.What is the value of y when x=5.7?

A
5
B
5.50
C
5.75
D
6
14

Which is the graph of g(x) = – 2?

Question illustration
A
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
Option A
B
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
Option B
C
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
Option C
D
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)
Option D
15

Which is the graph of the function f(x) =

Question illustration
A
Option
B
Option
C
Option
D
Option
16

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.
17

The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 9924x3 + 44x − 54x2 − 994x(____) − 9(____)What is the common factor that is missing from both sets of parentheses?

A
6x + 11
B
6x − 11
C
6x2 + 11
D
6x2 − 11
18

Which statements describe the domain and range of g(x)? Select two options.

A
The function g(x) is defined for all real numbers x.
B
The maximum value of the range is 4.
C
The maximum value of the domain is 3.
D
The range of g(x) is {y| –1 < y ≤ 4}.
E
The domain of g(x) is {x| –4 < x ≤ 3}.

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