Factorización de Polinomios: Conceptos y Ejercicios para Ingeniería Mecánica

Question 1

Factoriza el polinomio: x² + 6x + 9

Accepted Answer

(x + 3)²

Answer

(x - 3)²

Answer

(x + 3)(x - 3)

Answer

(x + 1)(x + 5)

Question 2

Factoriza el polinomio: x⁴ - 16

Accepted Answer

(x² - 4)(x² + 4)

Answer

(x - 2)(x + 2)(x² + 4)

Answer

(x - 4)(x + 4)(x² + 16)

Answer

(x² - 16)(x² + 16)

Question 3

Factoriza el polinomio x² + 2xy + y²:

Accepted Answer

(x + y)²

Answer

(x - y)²

Answer

(x + 2y)²

Answer

x(x + y)

Question 4

Factoriza la expresión x^2 - 9:

Accepted Answer

(x - 3)(x + 3)

Answer

x(x - 9)

Answer

No es factorizable

Answer

(x - 3)(x - 9)

Question 5

Factoriza la expresión x^2 + 8x + 16:

Accepted Answer

(x + 4)^2

Answer

No es factorizable

Answer

x(x + 8 + 16)

Answer

(x + 4)(x + 16)

Question 6

Emplea la regla de Ruffini para dividir 3x^3 - 7x^2 + 2x - 5 entre x - 1:

Accepted Answer

3x^2 - 4x + 5

Answer

x^3 - 7x^2 + 2x - 5

Answer

No es divisible

Answer

3x^3 + 7x^2 - 2x - 5

Question 7

Factoriza la expresión 8x^2 - 6xy + y^2:

Accepted Answer

(4x - y)(2x - y)

Answer

No es factorizable

Answer

2x(4x - y)

Answer

(8x - y)(x - y)

Question 8

Factoriza la expresión x^6 - 64:

Accepted Answer

(x - 2)(x + 2)(x^2 + 4)(x^2 - 4)

Answer

(x - 4)(x + 4)(x^2 - 2)

Answer

(x - 2)(x + 2)(x^2 + 4)

Answer

No es factorizable

Question 9

Factoriza el siguiente polinomio: x² - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 2)²

Answer

(x² + 4)(x² - 4)

Answer

(x - 4)(x + 4)

Question 10

Factoriza el siguiente polinomio: x² + 6x + 9

Accepted Answer

(x + 3)²

Answer

(x + 6)(x - 3)

Answer

(x - 6)(x + 3)

Answer

(x - 3)²

Question 11

Factoriza el siguiente polinomio: x² + 10x + 25

Accepted Answer

(x + 5)²

Answer

(x - 5)²

Answer

(x - 10)(x + 5)

Answer

(x + 10)(x - 5)

Question 12

Factoriza la expresión  x² - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

x² + 9

Answer

(x + 1)(x - 9)

Question 13

Factoriza el trinomio cuadrado perfecto x² - 4x + 4.

Accepted Answer

(x - 2)²

Answer

(x - 4)(x + 1)

Answer

(x - 1)(x + 4)

Answer

(x + 2)²

Question 14

Factoriza la expresión 2x³ - 4x² + 2x extrayendo el factor común.

Accepted Answer

2x(x² - 2x + 1)

Answer

x(2x² - 4x + 2)

Answer

x²(2x - 4)

Answer

2x²(x - 1)

Question 15

Factoriza completamente la expresión x⁴ - 16.

Accepted Answer

(x² + 4)(x + 2)(x - 2)

Answer

(x² + 4)(x + 4)(x - 4)

Answer

(x + 4)(x - 4)(x + 2)(x - 2)

Answer

(x² - 4)(x + 2)(x - 2)

Question 16

Utiliza la regla de Ruffini para encontrar un factor entero no trivial del polinomio x³ - 1.

Accepted Answer

x - 1

Answer

x² - 1

Answer

x² + 1

Answer

x + 1

Question 17

Factoriza el polinomio x³ + 2x² - 5x - 6.

Accepted Answer

(x + 3)(x + 1)(x - 2)

Answer

(x - 3)(x + 2)(x - 1)

Answer

(x - 3)(x - 1)(x - 2)

Answer

(x + 3)(x - 1)(x + 2)

Question 18

Factoriza el polinomio x⁴ - 2x² + 1.

Accepted Answer

(x² - 1)²

Answer

(x² + 1)²

Answer

(x + 1)⁴

Answer

(x - 1)⁴

Question 19

Factoriza el polinomio 2x³ + 3x² - 11x + 6.

Accepted Answer

(x + 2)(2x - 1)(x - 3)

Answer

(x - 2)(2x + 1)(x + 3)

Answer

(2x - 2)(x + 3)(x - 1)

Answer

(2x + 2)(x - 3)(x + 1)

Question 20

Factoriza la expresión x⁵ - 1.

Accepted Answer

(x - 1)(x⁴ + x³ + x² + x + 1)

Answer

(x - 1)(x⁴ - x³ - x² - x - 1)

Answer

(x + 1)(x⁴ - x³ + x² - x + 1)

Question 21

Factoriza el polinomio x³ - 8.

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x + 2)(x² - 2x + 4)

Answer

(x + 2)(x² + 2x - 4)

Answer

(x - 2)(x² - 2x - 4)