product of the GCF and its remaining factors.
3x + 6 = 3(x) + 3(2)
= 3(x + 2)
So, 3x + 6 = 3(x + 2).
5-8 Factor Linear Expressions
5. 2x – 15
Find the GCF of the pair of monomials.
1. 24, 48m
SOLUTION: Find the GCF of 2x and 15.
SOLUTION: Write the prime factorization of 24 and 48m.
Identify the common factors. The GCF of 24 and 48m is
There are no common factors, so 2x – 15 cannot be
factored.
6. 12x + 30y
.
SOLUTION: Find the GCF of 12x and 30y.
2. 32a, 48b
SOLUTION: Write the prime factorization of 32a and 48b.
Identify the common factors. The GCF of 32a and 48b is
The GCF of 12x and 30y is 2 · 3 or 6. Write each term as a product of the GCF and its remaining
factors.
12x + 30y = 6(2x) + 6(5y)
= 6(2x + 5y)
So, 12x + 30y = 6(2x + 5y).
.
3. 36k, 144km
SOLUTION: Write the prime factorization of 36k and 144km.
Identify the common factors. The GCF of 36k and 144k is
7. The area of rectangular dance floor is (4x – 8) square
units. Factor 4x – 8 to find possible dimensions of the
dance floor.
SOLUTION: Find the GCF of 4x and 8.
.
Factor the expression. If the expression cannot
be factored, write cannot be factored. Use algebra
tiles if needed.
4. 3x + 6
SOLUTION: Find the GCF of 3x and 6.
The GCF of 3x and 6 is 3. Write each term as a
product of the GCF and its remaining factors.
3x + 6 = 3(x) + 3(2)
= 3(x + 2)
So, 3x + 6 = 3(x + 2).
5. 2x – 15
SOLUTION: eSolutions
Manual
- Powered
by Cognero
Find the
GCF
of 2x and
15.
The GCF of 4x and 8 is 2 · 2 or 4. Write each term as
a product of the GCF and its remaining factors.
4x – 8 = 4(x) – 4(2)
= 4(x – 2)
So, the possible dimensions of the dance floor are 4
units by (x – 2) units.
8. The area of a rectangular porch is (9x + 18) square
units. Factor 9x + 18 to find possible dimensions of the
porch.
SOLUTION: Find the GCF for 9x and 18.
The GCF of 9x and 18 is 3 · 3 = 9. Write each term as a product of the GCF and its
remaining factors.
9x + 18 = 9(x) + 9(2)
= 9(x + 2)
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4x – 8 = 4(x) – 4(2)
= 4(x – 2)
the possible
of the dance floor are 4
5-8 So,
Factor
Lineardimensions
Expressions
units by (x – 2) units.
8. The area of a rectangular porch is (9x + 18) square
units. Factor 9x + 18 to find possible dimensions of the
porch.
SOLUTION: Find the GCF for 9x and 18.
The GCF of 9x and 18 is 3 · 3 = 9. Write each term as a product of the GCF and its
remaining factors.
9x + 18 = 9(x) + 9(2)
= 9(x + 2)
So, the possible dimensions of the porch are 9 units by
(x + 2) units.
9. 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
.
What was the cost of the visit for one person?
SOLUTION: Find the GCF of 6x and 12.
The GCF of 6x and 12 is 2 · 3 = 6. Write each term as
a product of the GCF and its remaining factors.
6x + 12 = 6(x) + 6(2)
= 6(x +2)
So, the cost of the visit for one person is (x + 2)
dollars.
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