Download PreAlgebra Find the greatest common factor

Name: ____________________________
Algebraic Expressions – Factoring Linear Expressions
1
Find the greatest common factor (GCF) of
each pair of monomials.
(a)
4x, 12x
(g)
63p, 84
(b)
18a, 20ab
(h)
30rs, 42rs
(c)
12cd, 36cd
(i)
60jk, 45jkm
(d)
12, 28c
(j)
40x, 60x
(e)
25x, 15xy
(k)
54gh, 72g
(f)
42mn, 14mn
(l)
100xy, 75xyz
2
3
Date: ________
PreAlgebra
6
Part A Factor each
Part B Simplify your
expression. If the expression
cannot be factored, write
cannot be factored.
answer in part A to check.
(a) 3x  9
(b) 12 x  7 y
Which pair of monomials has a GCF of 4a?
A
16a, 8a
C
16ab, 12b
B
18a, 8a
D
16ab, 12a
(c) 4 x  28
The Venn diagram shows the factors of 12
and 18x.
(d) 3x  33 y
What is the greatest common factor of the two
monomials?
4
5
A
2
C
6
B
3
D
36
(e) 4 x  35
Which of the following expressions cannot be
factored?
A
6  3x
C
15 x  10
B
7x  3
D
30 x  40
Explain how the GCF is used to factor an
expression. Use the term Distributive
Property in your response.
Sheet # 04-08
(f) 36 xy  24 y
(g) 14 x  16 xy
7
FIND THE ERROR
Rodney is factoring 90 x  15 . Find his
mistake and correct it.
expression below is equivalent to
10 Which
1
1
1
1
1
2 4 (2 2 𝑎) + 2 4 (1 2 𝑎) + 2 4 (2𝑎)?
A
8
Write two monomials whose greatest
common factor is 4m.
1 1
1
2 ∙ 2 𝑎 + 1 𝑎 + 2𝑎
4 2
2
1
1
1
B
2 4 (2 2 𝑎 + 1 2 𝑎 + 2𝑎)
C
1
2 (6 + 𝑎3 )
4
D
1
2 ∙ 6 + 𝑎3
4
_________ and _________
11 The three steps shown below were used to
9
Factor out the coefficient of the variable.
(a) 1
2
x4
(d) 5
6
x  30
find an expression equivalent to
2
(15𝑥 − 30𝑦) + 10𝑥.
5
Which expression could be used as Step 1?
B
2
(25𝑥 − 30𝑦)
5
6𝑥 − 12𝑦 + 10𝑥
C
6𝑥 − 30𝑦 + 10𝑥
D
15(𝑥 − 2𝑦) + 10𝑥
A
(b) 2
3
x6
(e) 2
5
x  16
12 Rewrite in simplest form.
2(5a  4b)  2b  6(2b  2a)
(c) 3
4
x  24
(f) 3
8
x  18
Simplified form: _________
Write the simplified expression in factored
form.
Factored form: _________
Name: ____________________________
Algebraic Expressions – Factoring Linear Expressions
13 Write an expression in factored form to
17
represent the total area of each rectangle.
A.
C.
Expression
B.
____________ Expression ____________
D.
Expression
____________ Expression ____________
Date: ________
PreAlgebra
Sheet # 04-09
Six friends visited a museum to see the new
holograms exhibit. The group paid for admission
to the museum and $12 for parking. The total
cost of the visit can be represented by the
expression $6x + $12. What was the cost, in
terms of x, of the visit for one person?
Answer __________
18 If the perimeter of a square is 14g + 28
inches, what is the length, in inches, of each
side of the square?
A
0.5g + 1
B
g+2
C
2g + 4
D
3.5g + 7
14 The drawing of the garden below has a total
area of (15 x  18) square feet. Find possible
dimensions of the garden.
19 The perimeter of an equilateral triangle is
3.6𝑥 − 15. What is the length of one side of
the triangle?
Answer __________
length: _________ width: ________
15 The area of a rectangular dance floor is
4 x  8 square units. Factor
4 x  8 to find
possible dimensions of the dance floor.
20 The perimeter of an equilateral triangle is
12𝑥 + 24. What is the length of one side of
the triangle?
Answer __________
21 If the perimeter of a square is 16g + 40
length: _________ width: ________
inches, what is the length, in inches, of each
side of the square?
16 The area of a rectangular porch is 9 x  18
square units. Factor 9 x  18 to find possible
dimensions of the porch.
Answer __________
22 If the perimeter of a square is 20g - 35
inches, what is the length, in inches, of each
side of the square?
length: _________ width: ________
Answer __________