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SKILL
Are You Ready?
55
Order of Operations
Teaching Skill 55
Objective Use the correct order of operations to
evaluate expressions.
Alternative Teaching Strategy
Objective Use the correct order of operations to
evaluate expressions.
Explain to students that order of operations
gives us a set of rules as to which operations
are carried out first when an expression involves
more than one operation.
Some students may benefit from manipulating
numbers and the order of operations.
Write the following numbers on the board: 2, 3, 4,
5, and 6. Tell students that you are going to use
each number exactly once, along with one set of
parentheses and one each of ⫹, ⫺, ⭈ , and ⫼ to
arrive at a final result of 4.
Review the correct order of operations with
students and the trick for remembering the order.
Direct students’ attention to the first example.
Demonstrate why having a set of rules is
necessary by working out the problem left to right
instead of using the correct order of operations.
(8 ⫺ 2 ⭈ 3 ⫽ 6 ⭈ 3 ⫽ 18) Ask: Do you get the
same result? (No)
Write: 6 ⫺ (2 ⭈ 3 ⫹ 4) ⫼ 5. Work through the
correct order of operations to demonstrate that
the result is 4.
⫽
⫽
⫽
⫽
Have students consider the second and third
examples. Before working through the examples,
ask a volunteer to list the operations they see in
each problem, in the order in which they would
be performed.
6
6
6
6
4
⫺
⫺
⫺
⫺
(2 ⭈ 3 ⫹ 4) ⫼ 5
(6 ⫹ 4) ⫼ 5
10 ⫼ 5
2
Instruct students to repeat this exercise using
the same numbers and the same rules to arrive
at a result of 3. Point out that they can have as
many, or as few, numbers inside the parentheses
as they need. (Students may arrive at different
results; one possible result is (2 ⫹ 3) ⫼ 5 ⫹ 6 ⫺
4.)
Have students complete the exercises.
PRACTICE ON YOUR OWN
In exercises 1–12, students evaluate expressions
using order of operations.
If students have trouble reaching an answer, have
them work in pairs. As students become more
comfortable, use larger numbers and mix up the
operations. For example, require the use of one
exponent, two additions, and two subtractions.
Be sure to specify whether any parentheses are
allowed.
CHECK
Determine that students know how to use
the correct order of operations to evaluate
expressions.
Students who successfully complete the Practice
on Your Own and Check are ready to move on
to the next skill.
Sample problems:
COMMON ERRORS
Students may always work from left to right and
forget to follow the correct order of operations.
1) Use the numbers 1, 2, 3, 4, and 5 with one
exponent, and one each of ⫹, ⫺, and ⭈
to arrive at a result of 13. No parentheses
3
allowed. Possible answer: 5 ⭈ 4 ⫺ 2 ⫹ 1.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Copyright © Holt McDougal.
All rights reserved.
2) Use the numbers 2, 3, 4, 6, and 10 with one
exponent, one set of parentheses, and one
each of ⫹, ⫺, and ⫼ to arrive at a result of 14.
2
Possible answer: 3 ⫹ 10 ⫼ (6 ⫺ 4).
121
Álgebra 1
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Nombre
DESTREZA
55
Fecha
Clase
¿Estás listo?
Orden de las operaciones
Orden correcto de las operaciones
1. Paréntesis
2. Exponentes
3. Multiplica / Divide
(de izquierda a derecha)
4. Suma / Resta
(de izquierda a derecha)
Una manera de recordar el orden: Pedro escribe muchos documentos sobre Rusia.
Ejemplo 1
Evalúa 8 ⫺ 2 ⭈ 3.
Ejemplo 2
2
Evalúa (6 ⫹ 4) ⫼ 5.
Ejemplo 3
3
Evalúa 2 ⫹ 4 ⭈ 3 ⫺ 6.
8 ⫺ 6
10 2 ⫼ 5
8⫹4 ⭈ 3⫺6
2
100 ⫼ 5
8 ⫹ 12 ⫺ 6
20
20 ⫺ 6
14
Practica por tu cuenta
Evalúa cada expresión.
1. (5 ⫹ 1) ⫺ 3
2. 8 ⭈ 8 ⫼ 16
3. 6 ⭈ 5 ⫹ 1
4. 24 ⫼ 3 ⫺ 5
5. (8 ⫹ 10) ⫼ 3
6. 20 ⫹ 1 ⫺ 7
2
7. 7 ⫹ 1
10. 8 ⫹ 7 ⭈ 5
8. 72 ⫼ 2
3
9. 21 ⫹ 15 ÷ 3
11. 3 ⭈ 6 ⫺ 2 ⭈ 9
2
12. (4 ⫹ 2) ⫼ 9
Comprueba
Halla el valor absoluto de cada expresión.
13. (6 ⫹ 10) ⫼ 4
14. 40 ⫺ 4 ⭈ 10
16. 15 ⫺ 3 ⫹ 10
17. 4 ⭈ 8 ⫼ 4
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2
122
15. 5 ⭈ 10 ⫼ 2
18. 8 ⭈ 5 ⫹ 3 ⭈ 6
Álgebra 1
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SKILL
Are You Ready?
59
Properties of Exponents
Teaching Skill 59
Objective Simplify expressions using properties
of exponents.
Alternative Teaching Strategy
Objective Simplify expressions using properties
of exponents.
Review with students the vocabulary at the top of
the student page and then the rule for multiplying
variables with the same base.
Some students may benefit from seeing numbers
and variables raised to exponents written in
expanded form.
2
2
4
Ask: Do the expressions x and y have the
2
same base? (No) What is the product of x
2
2 2
and y ? (x y ) Do you add the exponents?
(No) Why not? (The bases are not the same.)
Write the following on the board: 3 . Ask: How
would you write this expression without an
exponent? (3 ⭈ 3 ⭈ 3 ⭈ 3).
Next, write the following on the board:
4
2
3 ⭈ 3 . Ask a volunteer to come to the board and
rewrite the product without using any exponents.
(3 ⭈ 3 ⭈ 3 ⭈ 3 ⭈ 3 ⭈ 3) Ask: How would you write
6
4
2
this in exponential form? (3 ) Write 3 ⭈ 3
4⫹2
6
⫽3
⫽ 3 and point out that the result is the
same.
Review with students how to multiply expressions
that have numbers and variables. Ask: In the
5
expression 7x , what is the number 7 called?
(the coefficient)
Emphasize that to find the product of two
expressions, multiply the coefficients but add the
exponents of those variables that have the same
base.
7
Move on to variables. Write: x . Ask: How
would you write this expression without an
exponent? (x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x) Have the
students write the following problem on their
4
6
paper: x ⭈ x . Instruct them to rewrite the
problem without using exponents and to simplify
their final answer.
10
(x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⭈ x ⫽ x )
Also point out that when a variable does not have
a coefficient, it is understood to be 1. Likewise,
when a variable does not have an exponent, it is
understood to be 1.
Work through each of the examples and then have
students complete the practice exercises.
Finally, present an example with variables and
coefficients. Write on the board:
4
2
3n ⭈ 7n . Ask: What are the coefficients in
this problem? (3 and 7) What do you do with
them? (multiply them)
PRACTICE ON YOUR OWN
In exercises 1–12, students use properties of
exponents to simplify expressions.
CHECK
Determine that students understand properties of
exponents.
Instruct students to rewrite the problem without
using exponents and simplify.
6
(3 ⭈ 7 ⭈ n ⭈ n ⭈ n ⭈ n ⭈ n ⭈ n ⫽ 21n )
Students who successfully complete the Practice
on Your Own and Check are ready to move on
to the next skill.
Have students use this technique to simplify
the expressions below. Remind students that
if a variable does not have a coefficient or an
exponent, they are understood to be 1.
COMMON ERRORS
When multiplying variables with exponents,
students may multiply the exponents rather than
adding them.
5
3
7
10
When students are comfortable writing out and
simplifying expressions, have them redo the
a
problems using properties of exponents; x ⭈
b
a⫹b
x ⫽x
. Remind students that you multiply
coefficients and add exponents.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Copyright © Holt McDougal.
All rights reserved.
6
2x ⭈ 12x (24x ); 5n ⭈ 8n (40n );
2
4
6
5
5
10
6p ⭈ p (6p ); 7h ⭈ 7h (49h )
129
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DESTREZA
59
Propiedades de los exponentes
Vocabulario:
r exponente
r base
x
3
a
b
Regla: x x x
Para multiplicar variables con la misma base, suma los exponentes.
ab
Para multiplicar expresiones que incluyen números y variables:
• Multiplica los coeficientes. Si una variable no tiene coeficiente, se considera
que es 1.
• Suma los exponentes de las variables que son iguales. Si no se indica el
exponente de una variable, se considera que es 1.
3
Ejemplo 1: 5n 6n
(5 6)(n
11
) 30n
3
Ejemplo 2: 4x 7x
2
(4 7)(x
31
) 28x
5
Ejemplo 3: h k 3h k
4
(1 3)(h
35
)(k
2
12
8
) 3h k
3
Practica por tu cuenta
Simplifica cada expresión.
1. 2x 5x
2
2. 3a 7a
3
5. 5b c 5b c
9. 6t (3t )
3
3
6. 2xy (3xy)
2
10. w w w
2
3. 2 8mn
5
4. 15p 3pq
4
2
7. 16z (z)
2
8. d e 8de
4
11. 2r 11r (r )
12. 5x 10y xy
Comprueba
Simplifica cada expresión.
13. 15f 2f
3
17. p q 4pq
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2
14. 9 3x y
2
18. 3u 7u v
3
15. 20h (3h )
3
4
19. g g g
130
16. 7ab 7ab
20. 2y 8z yz
Álgebra 1
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SKILL
4
Are You Ready?
Greatest Common Factors
Teaching Skill 4
Objective Find the greatest common factor
of two expressions.
Alternative Teaching Strategy
Objective Find the greatest common factor using
prime factorization.
Explain to students that the greatest common
factor, or GCF, of two expressions is the largest of
the common factors that the expressions share.
Explain to students that monomial expressions
include a coefficient (number), one or more
variables (letters), or both.
Direct students to Steps 1–3.
Provide the following examples of monomial
3
2 2
expressions: 24x y and 80x y .
Ask: What are variables? (Variables are the
letters in an expression.)
Ask: What are the coefficients of these two
expressions? (24 and 80) Ask: What are the
variables in the expressions?
(x and y)
Ask: What is a coefficient? (A coefficient is the
number that precedes one or more variables in
an expression.)
Remind students that they can use prime
factorization to find the greatest common factor,
or GCF, of the coefficients. Work through the
process using 24 and 80.
Direct students to the example. Ask: What are
the coefficients of the two expressions? (18
and 30)
Ask: What is the smallest exponent of the
variable x in the two expressions? (1) What is
the smallest exponent of the variable y in the
two expressions? (2)
2 24
2 12
2 6
3
PRACTICE ON YOUR OWN
Review each step in the example.
2 80
2 40
2 20
2 10
5
Have students write the prime factorization of the
two numbers.
In exercises 1–9, students find the greatest
common factor for each pair of numbers or
expressions.
24 ⫽ 2 ⫻ 2 ⫻ 2 ⫻ 3
80 ⫽ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻ 5
Next have students line up matching factors
according to occurrence and circle complete
pairs.
CHECK
Determine that students know how to find the
greatest common factor for a pair of expressions.
24 ⫽ 2 ⫻ 2 ⫻ 2 ⫻
3
80 ⫽ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫻
Students who successfully complete the Practice
on Your Own and Check are ready to move on
to the next skill.
5
Explain that the GCF of the two numbers is the
product of the matched pairs only.
COMMON ERRORS
When the expressions include variables, students
choose the largest exponent of the variable,
rather than the smallest exponent.
Ask: What is the GCF of 24 and 80?
(2 ⫻ 2 ⫻ 2 ⫽ 8)
Explain that finding the GCF of the variables is
much easier–simply choose the smallest power of
each variable.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Ask: What is the GCF of the variables in the
2
two expressions and why? (x y since 2 is
the smallest exponent of x and 1 is the smallest
exponent of y)
3
2
2
2
The GCF of 24x y and 80x y is 8x y.
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Álgebra 1
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Clase
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DESTREZA
4
Máximo común divisor
Para hallar el máximo común divisor, o MCD, en expresiones algebraicas:
• Paso 1: Halla el MCD de los coeficientes de las expresiones.
• Paso 2: Halla el MCD de cada variable eligiendo la que tenga el menor
exponente.
• Paso 3: Escribe el MCD de las dos expresiones como el producto de los MCD
que hallaste en los Pasos 1 y 2.
4
2
2
Ejemplo: Halla el MCD de 18xy y 30x y .
Paso 1
Paso 2
Paso 3
4
2
2
coeficientes: 18 y 30
variables: xy y x y
factores de 18:
{1, 2, 3, 6, 9, 18}
menor exponente de x: x
factores de 30:
{1, 2, 3, 5, 6, 10, 15, 30}
menor exponente de y: y
MCD ⫽ 6
MCD ⫽ xy
MCD de los coeficientes: 6
MCD de las variables: xy
2
producto: 6 por xy
2
MCD ⫽ 6xy
2
2
2
Practica por tu cuenta
Halla el máximo común divisor de cada par de números o expresiones.
1. 8 y 20
3
2. 14 y 28
2
4. x y y x y
4
2
7. 16e f y 64ef
2
5. 18a y 42a
3
5
2
8. 28r st y 70rs
3. 32a y 60a
3
2
2
6. 4x y y 6x y
3
3
3
9. 10xyz y 5x z
Comprueba
Halla el máximo común divisor de cada par de expresiones.
4
2
11. 60e f y 24e f
10. 24 y 60
2
13. 15gh y 8g h
Copyright © Holt McDougal.
All rights reserved.
3
2
3
14. 12a b y 30a d
20
5
3
5
3
12. 12a y 28a
15. 50x y 40x
Álgebra 1
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Nombre
CAPÍTULO
9
Fecha
Clase
Enriquecimiento
Diviértete factorizando
¿Cuál es el número arábigo equivalente al número romano MMDCCXLVIII?
Para descubrir la respuesta, factoriza cada trinomio. Luego responde a las cuatro preguntas
al final de la página. Ubica cada respuesta en el espacio que esté sobre el número de
ejercicio correspondiente.
1. x 2 ⫺ 6x ⫹ 8
2. x 2 ⫹ x ⫺ 6
3. x 2 ⫺ 5x ⫹ 4
4. x 2 ⫹ x ⫺ 2
5. x 2 ⫺ 2x ⫺ 8
6. x 2 ⫹ x ⫺ 12
2
7. x ⫺ x ⫺ 12
8. x 2 ⫺ 3x ⫺ 4
9. x 2 ⫺ 3x ⫹ 2
10. x 2 ⫺ 8x ⫹ 16
11. x 2 ⫺ 2x ⫺ 15
12. x 2 ⫹ 5x ⫹ 6
13. x 2 ⫺ 5x ⫹ 6
14. x 2 ⫹ x ⫺ 20
15. x 2 ⫺ x ⫺ 2
16. x 2 ⫹ 4x ⫺ 5
17. x 2 ⫹ 2x ⫺ 8
18. x 2 ⫹ 3x ⫺ 10
1. ¿Cuántos de los trinomios tienen un factor de x ⫹ 1?
2. ¿Cuántos de los trinomios tienen un factor de x ⫺ 2?
3. ¿Cuántos de los trinomios tienen un factor de x ⫹ 3?
4. ¿Cuántos factores de x ⫺ 4 puedes ver?
1
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2
3
203
4
Álgebra 1
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Respuestas,
continuación
DESTREZA 53: RESPUESTAS
11. 0
Practica por tu cuenta
12. 12
1. 5
Comprueba
2. 18
13. 11
9
3. __
11
4. ⫺9
14. 2.3
5. 20
16. 25
6. 8
17. 13
7. 13
18. 0
1
8. ⫺ ___
25
19. 1.1
15. 10
20. 1
Comprueba
9. 4
10. 72
DESTREZA 55: RESPUESTAS
Practica por tu cuenta
11. ⫺7
1. 3
2
12. __
2. 4
5
13. 10
3. 31
14. ⫺12
4. 3
15. ⫺6
5. 6
1
16. __
6. 14
2
DESTREZA 54: RESPUESTAS
7. 50
Practica por tu cuenta
8. 9
1. 15
9. 26
2. 8
10. 43
3. 0.4
11. 0
4. 1.19
12. 4
5. 10
Comprueba
6. 4
13. 4
7. 0.75
14. 0
8. 0.7
15. 25
9. 6
16. 22
10. 7
17. 2
18. 58
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Álgebra 1
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Respuestas,
continuación
DESTREZA 56: RESPUESTAS
8. 0
Practica por tu cuenta
9. 11h
1. 5x ⫹ 30
10. ⫺9y ⫺ 9
2. 5z ⫺ 35
11. 10 ⫹ 10x
3. 2n ⫺ 4
12. 5 ⫺ 5u
4. 12 ⫹ 4k
13. 13y ⫹ 6x
5. 48 ⫺ 8y
14. 4
6. 6m ⫹ 18
Comprueba
7. 10p ⫹ 10
15. 10x
8. 60 ⫺ 3c
16. ⫺3c
9. 7q ⫺ 7
17. ⫺3a
10. 55 ⫹ 11t
18. 8.4z
11. 14 ⫹ 2b
19. 10m ⫹ 11
12. 36 ⫺ 9w
20. 8q ⫺ 5r
Comprueba
DESTREZA 58: RESPUESTAS
13. 12c ⫹ 24
Practica por tu cuenta
14. 15 ⫺ 5a
1. 5 ⫹ n
15. 25 ⫹ 25d
2. 15 restado de un número; 15 menos que un
número; la diferencia entre un número y
15; etc.
16. 50 ⫺ 10j
17. 4x ⫹ 12
3. C ⫽ 3(9.95) ⫹ 2(14.98)
18. 30 ⫹ 15y
4. P ⫽ 7 ⫹ 10 ⫹ s
19. 3g ⫺ 75
5. V ⫽ 12,000 ⫹ 500y
20. 9m ⫺ 9
DESTREZA 57: RESPUESTAS
2
6. n ⫽ 56 ⫺ 3w
Comprueba
7. n ⫺ 6
Practica por tu cuenta
1. 12x
8. C ⫽ 6(6.99) ⫹ 2(22.98)
2. 4m
9. A ⫽ 400 ⫹ 150m
3. 7a
2
DESTREZA 59: RESPUESTAS
4. ⫺7t
5. ⫺3b
6. 8d
Practica por tu cuenta
1. 10x
2
2. ⫺21a
7. ⫺x
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2
4
3. ⫺16mn
226
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Respuestas,
continuación
3
4. 45p q
5
5. 25b c
2
6. 6x y
4
13. ⫺6
2
14. ⫺4
5
7. 16z
3
15. 2
8. 8d e
2
9. ⫺18t
2
10. w
12. 0
DESTREZA 61: RESPUESTAS
Practica por tu cuenta
8
4
11. 22r
2
2
12. 50x y
2. 4x y
2
4
3. ⫺20a b
5
4. ___3
2t
Comprueba
13. 30f
2
2
f
5. ⫺ ___
3
2
14. ⫺27x y
15. 60h
4
3
2
16. 49a b
4
17. 4p q
2 3
6. ⫺3p q r
2
4
7. u v
2
2
4c
8. ___
5
d
3
18. ⫺21u v
19. g
2
1. 10m n
7
8
2
2
3
2
9. 144h k
2
20. ⫺16y z
10. ⫺1
2
11. 10xy z
DESTREZA 60: RESPUESTAS
wz
12. ⫺ ___
9
Practica por tu cuenta
1. 36
Comprueba
2. 28
13. 35s t
3. ⫺3
x
14. ⫺ ___
5y
4
4. ⫺27
4
15. ⫺8b c
5. 9
16. 5pq
6. ⫺2
4
3
7. ⫺10
5mn
17. ⫺ ____
3
8. 8
18. 36u w
9. ⫺6
19. ⫺10x y
3
8
Comprueba
4
2
7
20. __
f
10. 15
11. 2
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Respuestas,
continuación
16. no
8. compuesto, 2 ⫻ 6 ó 3 ⫻ 4 ó 1 ⫻ 12
17. {1, 17}
9. primo
18. {1, 3, 5, 9, 15, 45}
10. primo
19. {1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160}
11. compuesto, 11 ⫻ 11 ó 1 ⫻ 121
20. {1, 2, 4, 7, 14, 28}
12. primo
DESTREZA 4: RESPUESTAS
Comprueba
13. compuesto, 3 ⫻ 9 ó 1 ⫻ 27
Practica por tu cuenta
14. primo
1. 4
2. 14
15. compuesto, 9 ⫻ 9 ó 1 ⫻ 81
3. 4a
16. compuesto, 2 ⫻ 14 ó 4 ⫻ 7 ó 1 ⫻ 28
17. primo
2
4. x y
5. 6a
2
18. compuesto, 2 ⫻ 9 ó 3 ⫻ 6 ó 1 ⫻ 18
2
19. compuesto, 3 ⫻ 7 ó 1 ⫻ 21
6. 2x y
20. primo
7. 16ef
8. 14rs
DESTREZA 6: RESPUESTAS
9. 5xz
1. 9
Comprueba
2. 64
10. 12
3. 256
2
11. 12e f
12. 4a
4. 625
3
5. 4
13. gh
14. 6a
6. 12
3
15. 10x
7. 20
3
8. 9
9. no
DESTREZA 5: RESPUESTAS
10. sí, 1
Practica por tu cuenta
11. sí, 15
1. {1, 3, 11, 33}
12. no
2. {1, 23}
13. sí, 13
3. {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90}
14. sí, 14
4. {1, 2, 4, 5, 10, 20}
5. compuesto, 5 ⫻ 5 ó 1 ⫻ 25
15. no
6. compuesto, 2 ⫻ 23 ó 1 ⫻ 46
16. no
7. primo
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Enriquecimiento: Respuestas,
continuación
10. 625
Capítulo 10: Laberinto de multiplicaciones
11. 128
El dibujo sombreado es un avión.
12. 729
2
1. x ⫹ 3x
13. 387
2. x 2 ⫹ 8x ⫹ 7
2
3. x ⫹ 2x ⫺ 15
14. 169
15. 633
4. 2x 2 ⫺ 8x
16. 52
5. 8x ⫺ 8x 2
6. x 2 ⫺ 4x ⫺ 21
17. 243
7. 2x 2 ⫺ 11x ⫺6
18. 128
8. 27x ⫺ 3x
19. 864
2
9. 15x 2 ⫹ 2x ⫺1
20. 16
10. 12x 2 ⫹ 18x ⫹ 6
Capítulo 9: Diviértete factorizando
11. x 2 ⫺ 64
Respuesta: 2748
12. 45x ⫺ 20x
2
1. (x ⫺ 2)(x ⫺ 4)
13. 14x ⫺ 6
2. (x ⫺ 2)(x ⫹ 3)
14. x 2 ⫺ 13x ⫹ 30
3. (x ⫺ 1)(x ⫺ 4)
15. 30 ⫹ 7x ⫺ 2x 2
4. (x ⫹ 2)(x ⫺ 1)
16. 9x 2 ⫺ 49
5. (x ⫹ 2)(x ⫺ 4)
17. 10x ⫺ 4x
6. (x ⫺ 3)(x ⫹ 4)
18. 40x 2 ⫺ 43x ⫺ 6
7. (x ⫹ 3)(x ⫺ 4)
19. 9x 2 ⫺ 4
8. (x ⫹ 1)(x ⫺ 4)
20. 7x 2 ⫺ 32x ⫺ 15
9. (x ⫺ 2)(x ⫺ 1)
Capítulo 11: Los cuadrados de la buena suerte
2
10. (x ⫺ 4)(x ⫺ 4)
50
17
31
80
42
99
69
300
18
115
46
91
63
11. (x ⫺ 5)(x ⫹ 3)
72
94
65
89
550
10
8
121
97
950
59
150
73
12. (x ⫹ 2)(x ⫹ 3)
39
615
54
78
16
106
32
112
15
88
19
825
29
13. (x ⫺ 2)(x ⫺ 3)
125
60
215
211
225
117
377
76
9
82
105
52
85
22
800
81
1
12
250
21
47
196
25
13
115
45
815
4
114
37
116
6
53
7
500
101
525
36
68
51
400
43
113
93
58
40
325
650
715
71
11
28
16. (x ⫹ 5)(x ⫺ 1)
750
49
725
23
111
144
925
64
74
33
315
169
61
17. (x ⫺ 2)(x ⫹ 4)
86
98
14
625
900
107
256
109
30
100
5
700
56
18. (x ⫺ 2)(x ⫹ 5)
57
75
83
110
102
415
20
90
915
95
350
108
77
600
70
66
24
450
48
25
425
850
26
104
84
38
34
87
44
92
79
515
35
103
67
96
55
41
27
14. (x ⫹ 5)(x ⫺ 4)
15. (x ⫺ 2)(x ⫹ 1)
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Álgebra 1
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