Download ASSIGNMENT: Factoring using GREATEST COMMON FACTOR

NAME:________________________________________!
DATE: 02/06/14
ASSIGNMENT: Factoring using GREATEST COMMON FACTOR
DIRECTIONS: We factored numbers earlier in the year, and now we are going to factor
numbers AND variables. The concept is still the same. We want to break an expression
into simpler pieces. Factoring is like anti-distribution.
For example: The expression “12y³ + 15y²” has a few interesting things about it. First
we notice that the coefficients, “12” and “15” have a common factor of “3.”
Let’s “pull” that out or “factor” it from the expression. We now have: 3 (4y³ + 5y²)
Now we see that both terms have a common “y.” But exactly how many “y”s do they
share? They each have at least two “y”s, so let’s factor out a y². We now are left with:
3y² (4y + 5)
Is this completely factored? Is there anything left to do? Well, “4” and “5” don’t share
any common factors, and there are no more common variables. Therefore, we are done.
To check your answer, distribute and see if you get the same thing as you started.
Factor the following expressions utilizing the Greatest Common Factor method.
1.)#
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2.)
A: x(12x² – 6x + 3) #
D: already factored#
A: 16a²b(8b² – 1)
D: already factored
B: 6x(2x² – x + 1)
E: 2x(6x² – 3x + 2)#
B: 8a²b(3b² – 2)
E: 4a²b(6b² – 4)
C: 3x(4x² – 2x + 1)
F: 3x³(4x³ – 2x² + 1x)#
C: a²b(24b² – 16)
F: 2a²b(12b² – 8)
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4.) I have a special mathematical TV
with an area of 3x² + 24x in². What
are the dimensions of my TV?
A: 3xy(3x⁴y – x)#
D: already factored#
A: 3x(x + 8)
D: already factored
B: x²y(9x³y – 3)
E: 3x⁵y²(3 – xy)# #
B: 3(x² + 8x)
E: 3x²(1 + 8x)
C: x⁵y²(9xy – 3xy)
F: 3x²y(3x³y – 1) #
C: x(3x + 24)
F: 3x(1 + 8x)
5.) 45g⁵h⁴ – 35g³h³ + 20g²h³
A: 9g²h³(5g³h – 7g + 4)#
B: 9gh(5g⁴h³ – 7g²h² + 4gh²)#
C: g²h³(45g³h – 35g + 20)
D: 5(9g⁵h⁴ – 7g³h³ + 4g²h³)
E: 5g²h³(9g³h – 7g + 4) #
F: already factored
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