Expresiones algebraicas: conceptos básicos y operaciones

Question 1

Factoriza la siguiente expresión algebraica: x^2 - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 2)^2

Answer

No se puede factorizar

Answer

(x + 2)^2

Question 2

Identifica el término independiente del siguiente polinomio: 3x^2 - 5x + 7

Accepted Answer

7

Answer

0

Answer

5

Answer

3

Question 3

Determina el coeficiente del término x^2 en el siguiente polinomio: 2x^3 - 5x^2 + 7x - 1

Accepted Answer

-5

Answer

-2

Answer

7

Answer

2

Question 4

Simplifica la expresión: 2x + 3y - x + 2y

Accepted Answer

x + 5y

Answer

2x + 5y

Answer

x + 3y

Answer

3x + 5y

Question 5

Factoriza la expresión: x² - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

No se puede factorizar

Answer

(x + 9)(x - 1)

Question 6

Simplifica la expresión: (x + 2)² - (x - 1)²

Accepted Answer

4x + 5

Answer

No se puede simplificar

Answer

4x - 5

Answer

x² + 5

Question 7

Factoriza la expresión: x³ - 8

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x - 2)³

Answer

(x + 2)(x² - 2x + 4)

Answer

No se puede factorizar

Question 8

Factoriza la expresión: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

x(x + 3)

Answer

(x + 9)(x - 9)

Answer

(x - 3)^2

Question 9

Expande el cubo de un binomio: (x + 2)^3

Accepted Answer

x^3 + 6x^2 + 12x + 8

Answer

x^3 + 6x^2 + 8x + 4

Answer

x^3 + 4x^2 + 8x + 4

Answer

x^3 + 4x^2 + 4x + 8

Question 10

Identifica el coeficiente numérico del término de segundo grado (x²) en la expresión: 3x^2 - 2x + 1

Accepted Answer

3

Answer

0

Answer

1

Answer

2

Question 11

Aplica la identidad algebraica de la diferencia de cuadrados para reducir la expresión: (x + y)^2 - (x - y)^2

Accepted Answer

4xy

Answer

2x^2 - 4xy + 2y^2

Answer

x^2 + y^2

Answer

2x^2 + 4xy + 2y^2

Question 12

Simplifica la expresión radical: √(16x^2)

Accepted Answer

4x

Answer

16x

Answer

2x

Answer

8x

Question 13

¿Cuál de las siguientes expresiones es un monomio?

Accepted Answer

3x

Answer

2x * 3y

Answer

x^2 - 5

Answer

x + 2

Question 14

¿Cuál es el grado del polinomio: 2x^3 - 5x^2 + 3?

Accepted Answer

3

Answer

1

Answer

4

Answer

2

Question 15

Divide el polinomio: (x^2 - 4) ÷ (x - 2)

Accepted Answer

x + 2

Answer

x - 2

Answer

x^2 + 2x + 4

Answer

2x + 4

Question 16

Factoriza el polinomio: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)^2

Answer

(x - 9)(x + 9)

Answer

(x - 3)^2

Question 17

Simplifica la expresión algebraica: **2x + 3y - x - y**

Accepted Answer

**x + 2y**

Answer

x - y

Answer

2x - 2y

Answer

x - 2y

Question 18

¿Cuál de las siguientes expresiones es equivalente a **(x + 2)(x - 3)**?

Accepted Answer

**x^2 - x - 6**

Answer

x^2 + x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 19

Resuelve la ecuación: **2x - 5 = 11**

Accepted Answer

**8**

Answer

12

Answer

10

Answer

6

Question 20

¿Cuál es el coeficiente del término **x^2** en la expresión algebraica: **3x^2 - 2x + 5**?

Accepted Answer

**3**

Answer

2

Answer

0

Answer

5

Question 21

Factoriza la expresión algebraica: **x^2 - 9**

Accepted Answer

**(x + 3)(x - 3)**

Answer

(x^2 - 3)(x + 3)

Answer

(x^2 + 3)(x - 3)

Answer

(x - 3)(x + 3)

Question 22

Simplifica la fracción algebraica: **(x^2 - 4) / (x - 2)**

Accepted Answer

**x + 2**

Answer

(x - 2)^2

Answer

(x + 2)(x - 2)

Answer

x - 2

Question 23

¿Cuál de las siguientes expresiones es una desigualdad lineal?

Accepted Answer

**2x + 1 > 5**

Answer

x^2 - 4 < 0

Answer

(x - 1)(x + 2) > 0

Answer

x^2 + 2x - 3 = 0

Question 24

Resuelve la desigualdad: **x - 3 > 2**

Accepted Answer

**x > 5**

Answer

x < 5

Answer

x > 1

Answer

x < 1

Question 25

¿Cuál de las siguientes expresiones es una función lineal?

Accepted Answer

**f(x) = 2x + 1**

Answer

f(x) = (x - 1)(x + 2)

Answer

f(x) = x^2 + 2x - 3

Answer

f(x) = x^2 - 4

Question 26

Halla la pendiente de la función lineal: **f(x) = -2x + 5**

Accepted Answer

**-2**

Answer

2

Answer

5

Answer

0

Question 27

Simplifica la expresión algebraica: x + 2 - x - 1

Accepted Answer

1

Answer

1 - x

Answer

x + 1

Answer

x - 1

Question 28

Multiplica el monomio 2x²y por 3.

Accepted Answer

6x²y

Answer

3x²

Answer

8x²y

Answer

2x³y

Question 29

Divide el polinomio x³ - 4x² + 4x - 8 entre (x - 2).

Accepted Answer

x² - 2x + 4

Answer

x³ - 2x² + 4

Answer

x² - 4x + 8

Answer

x² + 2x - 4

Question 30

Factoriza el polinomio x² - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

No se puede factorizar

Answer

(x - 3)²

Answer

(x + 9)(x - 9)

Question 31

Determina el grado del polinomio x⁴ - 2x³ + 3x - 5.

Accepted Answer

4

Answer

5

Answer

2

Answer

3

Question 32

Simplifica la expresión radical √(16x²y⁴).

Accepted Answer

4xy²

Answer

16xy⁴

Answer

2xy

Answer

8xy²

Question 33

¿Cuál es el grado de la expresión algebraica 5x³ - 2x² + 7x - 1?

Accepted Answer

3

Answer

2

Answer

4

Answer

1

Question 34

Identifica la expresión algebraica que representa la suma de un número y su doble.

Accepted Answer

x + 2x

Answer

2x² + x

Answer

x² + 2x

Answer

x - 2x

Question 35

Simplifica la expresión: (x + y)²

Accepted Answer

x² + 2xy + y²

Answer

x² - y²

Answer

x² - 2xy + y²

Answer

x² + y²

Question 36

Si el perímetro de un rectángulo es 20 cm y la longitud es 6 cm, ¿cuál es la expresión algebraica que representa el ancho del rectángulo?

Accepted Answer

10 - l

Answer

l - 10

Answer

l - 20

Answer

20 - l

Question 37

Simplificar la expresión (2x + 3y) - (x - y):

Accepted Answer

x + 4y

Answer

3x + 2y

Answer

x + 2y

Answer

2x - 2y

Question 38

Multiplicar (3x - 2y) por (2x + y):

Accepted Answer

6x^2 - 4xy - 2y^2

Answer

6x^2 - 2xy - 4y^2

Answer

6x^2 + 2xy - 4y^2

Answer

6x^2 + 4xy - 2y^2

Question 39

Dividir (6x^2 - 4xy + 2y^2) entre (2x - y):

Accepted Answer

3x - 2y

Answer

3x + 2y

Answer

2x - 3y

Answer

2x + 3y

Question 40

Factorizar la expresión 4x^2 - 9:

Accepted Answer

(2x - 3)(2x + 3)

Answer

(2x + 3)(2x - 3)

Answer

(4x - 9)(x + 1)

Answer

(4x + 9)(x - 1)

Question 41

Resolver la ecuación 2x + 5 = 13:

Accepted Answer

4

Answer

8

Answer

6

Question 42

¿Cuál de las siguientes expresiones es una identidad algebraica?

Accepted Answer

(x + y)^2 = x^2 + y^2

Answer

(x - y)^3 = x^3 - y^3

Answer

(x + y)^3 = x^3 + y^3

Answer

(x - y)^2 = x^2 - y^2

Question 43

Simplificar la expresión (2x^2y)^3:

Accepted Answer

8x^6y^3

Answer

4x^6y^6

Answer

4x^6y^3

Answer

2x^6y^6

Question 44

Resolver la inecuación x^2 - 4 < 0:

Accepted Answer

-2 < x < 2

Answer

x > -2 o x < 2

Answer

x < -2 o x > 2

Answer

-2 < x < 4

Question 45

Hallar el valor de x en la ecuación x + |x| = 6:

Accepted Answer

3 o -3

Answer

6 o -6

Answer

2 o -2

Answer

4 o -4

Question 46

Expresar la suma de dos números enteros consecutivos como una expresión algebraica:

Accepted Answer

n + (n + 1)

Answer

2n + 1

Answer

n + 2

Answer

2n