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
Date: _________
PreAlgebra
6
Part A Factor each
expression. If the expression
cannot be factored, write
cannot be factored.
(a) 3 x + 9
(b) 12 x + 7 y
2
3
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) 3 x + 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 # 04-09
(f) 36 x + 24
(g) 14 x − 16 xy
Part B Simplify your
answer in part A to check.
7
Write an expression in factored form to
represent the total area of each rectangle.
A.
C.
Expression
____________
Expression
Rodney is factoring 90 x − 15 . Find his mistake
and correct it.
____________
13 Write two monomials whose greatest common
factor is 4m.
D.
B.
12 FIND THE ERROR
_______________________
14 Factor out the coefficient of the variable.
(a) 1
2
x+4
(d) 5
6
x − 30
____________ Expression ____________
The drawing of the garden at the right has a
total area of (15 x + 18) square feet. Find
possible dimensions of the garden.
Expression
8
(b) 2
3
x+6
(e) 2
5
x + 16
length: _________ width: ________
9
10
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.
length: _________ width: ________
The area of a rectangular porch is
(9 x + 18) square units. Factor 9 x + 18 to find
possible dimensions of the porch.
(c) 3
4
x − 24
(f) 3
8
x + 18
15 Rewrite in simplest form.
2(5a − 4b) + 2b − 6(2b − 2a )
11
length: _________ width: ________
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?
Simplified form: _________
Write the simplified expression in factored
form.
Answer __________
Factored form: _________