Question

Porfaaaa
Ayudenmeeee

Answer 1

En el primer ejercicio la C y la D estan al reves, las demas estan bien.
En el segundo la respuesta es la b o la d no estoy segura 
En el tercer ejercicio estan bien 

Answer 2

P(x) = 3X² + 2X - 1; Q(x) = 6X³ + 13X² + 4X - 3

P(x) + Q(x) = (3X² + 2X - 1) + (6X³ + 13X² + 4X - 3)

P(x) + Q(x) = 3X² + 2X - 1 + 6X³ + 13X² + 4X - 3

P(x) + Q(x) = 6X³ + 16X² + 6X - 4

Q(x) - P(x) = (6X³ + 13X² + 4X - 3) - (3X² + 2X - 1)

Q(x) - P(x) =  6X³ + 13X² + 4X - 3 - 3X² - 2X + 1

Q(x) - P(x) = 6X³ + 10X² - 2X - 2

P(x)*Q(x) = [(6X³ + 13X² + 4X - 3)(3X² + 2X - 1)]

P(x)*Q(x) = [18X^5 + 12X^4 - 6X³ + 39X^4 + 26X³ - 13X² + 12X³ + 8X² - 4X -9X² - 6X + 3]

P(x)*Q(x) =  18X^5 + 51X^4 + 32X³ - 14X² - 6X + 3

[P(x)]² = [3X² + 2X - 1]² = (3X² + 2X - 1)(3X² + 2X - 1)

[P(x)]² = [9X^4 + 6X³ - 3X² + 6X³ + 4X² - 2X - 3X² - 2X + 1]

[P(x)]² = [9X^4 + 12X³ - 2X² - 4X + 1]

2) (X^6 - 1)/(X - 1)

(X^6 - 1) = (X³ - 1)(X³ - 1)

(X³ + 1) = (X + 1)(X² - X + 1)

(X³ - 1) = (X - 1)(X² + X + 1)

(X^6 - 1) = [(X + 1)(X² - X + 1)(X - 1)(X² + X + 1)]

(X^6 - 1)/(X - 1) = [(X + 1)(X² - X + 1)(X - 1)(X² + X + 1)]/(X - 1)

[(X + 1)(X² - X + 1)(X - 1)(X² + X + 1)]/(X - 1) (Cancelo el (X - 1) arriba y abajo)

(X + 1)(X² - X + 1)(X² + X + 1) = (X^6 - 1)/(X - 1)

Vamos por partes:

(X + 1)(X² - X + 1) = X³ - X² + X + X² - X² + 1 = X³ + 1

(X³ + 1)(X² + X + 1) = X^5 + X^4 + X³ + X² + X + 1

= X^5 + X^4 + X² + X² + X + 1

(X^6 - 1)/(X - 1) = X^5 + X^4 + X² + X² + X + 1

3)

a) X^4 - 1 = (X² - 1)(X² + 1)

(X² - 1) = (X + 1)(X - 1)


X^4 - 1 = (X + 1)(X - 1)(X² + 1)

b) X^4 - 10X³ + 35X² - 50X + 24 


X^4 - 10X³ + 35X² - 50X + 24 (Divido entre X - 1)

X^4 - 10X³ + 35X² - 50X + 24 = (X - 1)(X³ + 26X - 9X² - 24)

(X³ + 26X - 9X² - 24) (Divido entre X - 2)

X³ + 26X - 9X² - 24 = (X - 2)(X² - 7X + 12)

(X² - 7X + 12) = (X - 3)(X - 4)


X^4 - 10X³ + 35X² - 50X + 24  = (X - 1)(X - 2)(X - 3)(X - 4)

c) X³ + 5X² + X + 5

(X³ + 5X²) + (X + 5)

X²(X + 5) + (X + 5)

(X + 5)(X² + 1)

X³ + 5X² + X + 5 = (X + 5)(X² + 1) 

d) 12X³ - 16X² - 20X + 8

12X³ - 16X² - 20X + 8

4(3X³ - 4X² - 5X + 8)

4[(3X³ - 4X² - 5X + 8) Divido entre (X + 1)]

4[(X + 1)(3X² - 7X + 2)]

(3X² - 7X + 2) = 3X² - X - 6X + 2

(3X² - X) + (-6X + 2)

X(3X - 1) - 2(3X - 1)

(X - 2)(3X - 1)

(3X² - 7X + 2) = (X - 2)(3X - 1)

4[(X + 1)(X - 2)(3X - 1)]

12X³ - 16X² - 20X + 8 = 4[(X + 1)(X - 2)(3X - 1)]