Sofia Prada 7 2

Factorization, common factors and rational functions

Criterion B:

Achievement level Level descriptor Task Specific
The student does not reach a standard described The student does not reach a standard described by any
0
by any of the descriptors below. of the descriptors below
1. The student is able to match the similar
The student is able to:
expressions from table 1

1–2 i. apply, with teacher support, mathematical 2. The student is able to match similar
problem-solving techniques to discover simple expressions from tables 1 and 2
patterns

3. The student is able to identify similar

expressions from tables 1 and 2; describes,
with some degree of accuracy, the relation
The student is able to: between the similar expressions

3–4 4. The student is able to identify the common

i. apply mathematical problem-solving techniques
factor of table 4 and describe, with some
to discover simple patterns
degree of accuracy, how to identify the
common factor

5. The student is able to identify the common

The student is able to: factor of tables 4 and 5; describes, with some
degree of accuracy, how to identify the
common factor
i. select and apply mathematical problem-solving
5–6 techniques to discover patterns 6. The student is able to match similar
expressions from table 3 and describes, with
ii. describe patterns as relationships and/or some degree of accuracy, how to identify
general rules consistent with findings similar expressions

The student is able to: 7. The student is able to find the common factor
in table 6 and describes how to identify the
common factor
i. select and apply mathematical problem-solving
7–8 techniques to discover patterns 8. The student is able to find the common factor
in table 7 and describes how to identify the
ii. describe patterns as relationships and/or common factor
general rules consistent with correct findings



Identifying similar expressions

Table 1: Match the similar expressions from both lists

7! ! + 3! 77! ! − 44!"
!" + 2! 2ℎ − !
! ! 3!" + 6!
2! − 4! !
5 − 9! 14! ! + 6!
! − !" 10!! − 5!"
12ℎ − 6! 50 − 90!
7! ! − 4!" 8! − 8!"
2!! − !" ! ! − 2! ! !


Describe how you identified the similar expressions
I identified the like terms by checking and matching the same
variables which also had the same exponent, even if the coefficients
are different. The coefficients on the left and the ones on the right are
similar since if you multiply by the same number they match. The
coefficients must be multiplied by the same factor.



Table 2: Match the similar expressions from both lists


7! ! + 3! ! ! − !"
! !
!! + 2! 7! ! + 3!
! ! 12ℎ − 6!
2! − 4! !
5! − 9! ! !" + 2!
! !
! ! − ! ! 7! ! − 4!"
!
12ℎ − 6ℎ! 2! ! − 4! ! !
7! ! ! ! − 4!! ! 2!! − !"
2! − ! 5 − 9!


Describe how you identified the similar expressions
I identified the like terms by checking and matching the similar
variables which sometimes had similar exponents, even if the
coefficients were different. The coefficients on the left and the
ones on the right are similar since both could be divided or
subtracted by the same number to get the answer on the other
side. The coefficients must be multiplied by the same factor.

Table 3: Match the similar expressions from both lists

21! ! + 9! ! 5 − 9!
! ! + 2!
4! + 8!"
! ! − 2! ! ! 20! − 10!
15! − 27! ! 12ℎ − 6!
7 − 7! ! − !"
2ℎ! − !" 2! ! − 4! ! !
35! ! − 20! ! ! 7! ! + 3!
!
2! − !" 7! ! − 4!"


Describe how you identified the similar expressions
I identified the similar expressions by checking and matching the
similar variables which sometimes had similar exponents, even if the
coefficients were different. The coefficients on the left and the ones on
the right are similar since both could be divided or subtracted by the
same number to get the answer on the other side. The coefficients
must be divided by the same factor.
























 Identifying common factors

Table 4: Find the common factor from both expressions

Expression 1 Expression 2 Common factor
2! + ! 4! + 2! 2! + !
! !
6! + 4! 9! + 6! 3!! + 2!
3! − 3! ! − ! e t costed
40! − 10! 4! − !
9 − 2!" 36 − 8!"
Ur n
g 2py
12! ! − 8! 18! ! − 12!
700! ! + 500 7! ! + 5
Gf4g
28! ! − 16!" 7! ! − 4!"
7 21 2
5
7
Xy

Based on the previous table, describe how to identify the common factor
1. Identify the greatest common factor.

2. For each variable, the least exponent is the common factor.

3. Identify the common factor.

Table 5: Find the common factor from both expressions

Expression 1 Expression 2 Common factor
5! − 9!" 5! − 9! ! 5 − 9!
! ! ! + 2!
! + 2!" !" + 2!
! 2! − !
2! − !"
2ℎ! − !" 2ℎ! − !" Zp
q
7 − 7! 7! − 7!"
2h n
4! ! − 8! ! ! 4! ! − 8! ! !
7p
7 5
4 83
7! ! + 3! ! 7! ! + 3! y
7 x't 3
7! ! − 4! ! ! 7! ! − 4!"

724xy
Based on the previous table, describe how to identify the common factor
1. Identify the greatest common factor.

2. For each variable, the least exponent is the common

factor.

3. Identify the common factor.

Table 6: Find the common factor from both expressions

Expression 1 Expression 2 Common factor
2!! + !" 4! + 2! 2! + !
! 4! + 4! ! + !
3! + 3!"
! 12!" − 15!"
4! − 5!"
He Sf
3ℎ! − 4!! 6ℎ! ! − 8!! !
14!" − 21!" 42!" − 63!"
342 4g i
24!" − 36!" 2!" − 3!"
14 21
2k 3L
20!! − 30!! 40!! − 60!!
2ms 30ns

Based on the previous table, describe how to identify the common factor
1.
Identify the greatest common factor.

2.
For each variable, the least exponent is the common
factor.

3.
Identify the common factor.





Table 7: Find the common factor from both expressions

Expression 1 Expression 2 Common factor
! ! ! ! ! ! ! !
40! ! − 80! ! 8! ! − 16! ! 8! ! ! ! − 16! ! ! !
! ! ! ! ! !! ! !!
200! ! − 500! ! 2! ! − 5! ! 2! ! !! − 5! ! !!
15!! ! ! − 9!! ! ! 10!! ! ! − 6!! ! ! 50133 30,35
! ! ! ! !
7!" − 8! ! 21! ! − 24! !
79W 892W
! !
14! ! − 7! ! ! !
12! ! ! ! − 6! ! ! ! 2 43 43
8! ! ℎ! − 6! ! ℎ 20! ! ℎ! − 15! ! ℎ!
5!!" ! ! − 5! ! ! ! 6!!" ! ! − 6! ! ! !
UdZha 3d h
b V b2v3

Based on the previous table, describe how to identify the common factor
Identify the greatest common factor.

1.
For each variable, the least exponent is the common factor.

2.
Identify the common factor.
3.