Download 11.2 Factor by GCF 2016 ink.notebook

11.2 Factor by GCF 2016 ink.notebook
April 04, 2017
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Page 136
11.2 Factor by GCF
(What's in Common)
Lesson Objectives
Standards
Lesson Page 137
11.2 Factoring by GCF
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11.2 Factor by GCF 2016 ink.notebook
Lesson Objectives
Standards
Lesson
A.SSE.1 I will find the GCF of an expression A.SSE.2 I will rewrite an expression into factored form by pulling out the GCF Press the tabs to view details.
April 04, 2017
Lesson Objectives
Standards
Lesson A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a) Factor a quadratic expression to reveal the zeros of the function it defines.
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Find the GCF of each set of monomials. Characteristics:
My Definition:
If there are NO
common factors
GCF = 1
numbers. Biggest number
They
are
said to be
that can be evenly
GCF
relatively prime.
divided into both.
Greatest Common
Greatest number that
is a factor of BOTH
Example:
Factor
12 and 18
GCF = 6
2 and 7
15x and 27x
Biggest number that goes
INTO both
Use the smallest exponent
for variables.
1. 4a7b, 28ab
2. 49x, 343x2
3. 96y, 12x, 8y
4. 12a, 18abc
Counterexample:
12 and 18
LCM= 36
GCF = 1
2
12 and 18
3 is a factor but not
GCF = 3x
the biggest one
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11.2 Factor by GCF 2016 ink.notebook
April 04, 2017
*Always check to
see if possible*
Answer will be in
the form:
*Always the FIRST
step in any factoring
problem*
__(_______)
4x2 ­ 12x
See what you
can divide
EVERY term by.
4x2 ­ 12x
4x
4x
final answer
4x (x ­ 3)
What you What is left divided by when you are done dividing
4x2 ­ 12x + 8
See what you
can divide
EVERY term by.
4x2 ­ 12x + 8
4
4
4
final answer
4(x2 ­ 3x + 2)
What you What is left divided by when you are done dividing
Look for the GCF & rewrite in factored form.
5. 2x + 8
What is the biggest number you can take out of both terms? ( )
6. n2 – 13n
( )
7. –4k2 + 5k
8. 3x2 – 15x
9. 4m2 + 2m
10. –32v2 – 24v
Can you also take out any letters?
(smallest exponent)
Remember, The FIRST term can
NOT be negative. You must
factor the negative out.
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11.2 Factor by GCF 2016 ink.notebook
April 04, 2017
Look for the GCF & rewrite in factored form.
11. 3m3 – 7m2 – m
12. 100p3 + 25p2 + 75p
13. 3p2r2 + 6pr + p 14. 4a2b2 + 16ab + 12a
On Your
Whiteboards
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11.2 Factor by GCF 2016 ink.notebook
a)
24cd3, 48c2d
b) 30gh2, 42g2h
On the
Worksheet
Look for the GCF & rewrite in factored form.
c) 3x2 + 27x
d) 5a2 – 30a
e) x + x2y + x3y2
f) 63z3 ­ 15z2 + 33z
Homework
Homework
Homework
Hint
Find the GCF of each set of monomials. April 04, 2017
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
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11.2 Factor by GCF 2016 ink.notebook
Use distributive property to simplify.
April 04, 2017
Find the GCF of each set of monomials. 5. 24cd3, 48c2d
1. 2x(x + 3)
2x2 + 6x
3. 5y(y + 1)
5y2 + 5y
2. 2c(3c – 4)
6c2 ­ 8c
4. 3n(2n – 1)
6n2 ­ 3n
Find the GCF of each set of monomials. 7. 12qr, 8r2
6. 30gh2, 42g2h
8. 10ab, 25a
Find the GCF of each set of monomials. 9. 25x3, 45x4, 65x2
10. 26n2, 32n, 44n4
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11.2 Factor by GCF 2016 ink.notebook
Look for the GCF & rewrite in factored form.
11. 21b – 15a
12. 14c2 + 2c
13. 5z2 + 10z
14. 2k2 + 4k
17. 4a2b2 + 2a2b – 10ab2
18. 12jk2 + 6j2k + 2j2k2
April 04, 2017
15. 16t – 40y
19. 10g2h2 + 9gh2 – g2h
16. 30v + 50x
20. 5c2v – 15c2v2 + 5c2v3
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11.2 Factor by GCF 2016 ink.notebook
21. 8r2 + 12r
22. 5gf2 + g2f + 15gf
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23. 27cd2 – 18c2d2 + 3cd
24. 18r3t2 + 12r2t2 – 6r2t
Rewrite each expression using only positive exponents. No Decimals.
25. We are going to start a new computer software company. The cost to obtain the rights to a new computer game and a CD burner is $45,000. It also costs $5 for materials and labor for each game to be packaged for sale. We are planning to sell our games for $20 each. How many games must we sell in order to break even? Write an equation, solve by showing all work, and label your answer.
26. –2pq–8
27. x–9 ¥ x3 28. (3x)–2
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11.2 Factor by GCF 2016 ink.notebook
April 04, 2017
Answers:
1) 2x2 + 6x 3) 5y2 + 5y 5) 24cd 7) 4r 9) 5x2 11) 3(7b – 5a) 13) 5z(z + 2) 15) 8(2t – 5y) 17) 2ab(2ab + a – 5b) 19) gh(10gh + 9h – g) 21) 4r(2r + 3) 23) 3cd(9d – 6cd + 1)
25) C = 45000 + 5x, R = 20x, 45000 + 5x = 20x, x = 3000 games 9