Question

1-) Fatore cada um dos polinômios: ( Agrupamento)

a) ab - b + 2a – 2 f) am + bm + an + bn

b) x6 + 2x4 + ax² + 2ª g) ax + 5x + ay + 5y

c) by² - 2b + cy² - 2c h) a³ - a² + a - 1

d) x³ - 10x² + xy - 10y i) 10a³b - 5ab³ + 6a² - 3b²

e) 5c + 5 - ac – a j) 3a - 6y + ab - 2by

k) ax – ay + bx – by = l) 5ax – 5ay + bx – by =

m) x² + 5x + ax + 5a = n) 6a² + 2ab – 3ac – bc =

o) t³ + t² – 7t – 7 = p)

4 – x³ – 9x + 9 =

q) 2b² + 2 – b²k – k = r) bx² – 2by + 5x² – 10y =

s)

5 + a³ + 2a² + 2 = t) cx + x + c + 1 =


me ajudem por favor ​

Answer 1

Explicação passo-a-passo:

a)

ab - b + 2a - 2

= b.(a - 1) + 2.(a - 1)

= (a - 1).(b + 2)

b)

x⁶ + 2x⁴ + ax² + 2a

= x⁴.(x² + 2) + a.(x² + 2)

= (x² + 2).(x⁴ + a)

c)

by² - 2b + cy² - 2c

= b.(y² - 2) + c.(y² - 2)

= (y² - 2).(b + c)

d)

x³ - 10x² + xy - 10y

= x².(x - 10) + y.(x - 10)

= (x - 10).(x² + y)

e)

5c + 5 - ac - a

= 5.(c + 1) - a.(c + 1)

= (c + 1).(5 - a)

f)

am + bm + an + bn

= m.(a + b) + n.(a + b)

= (a + b).(m + n)

g)

ax + 5x + ay + 5y

= x.(a + 5) + y.(a + 5)

= (a + 5).(x + y)

h)

a³ - a² + a - 1

= a².(a - 1) + 1.(a - 1)

= (a - 1).(a² + 1)

i)

10a³b - 5ab³ + 6a² - 3b²

= 5ab.(2a² - b²) + 3.(2a² - b²)

= (2a² - b²).(5ab + 3)

j)

3a - 6y + ab - 2by

= 3.(a - 2y) + b.(a - 2y)

= (a - 2y).(3 + b)

k)

ax - ay + bx - by

= a.(x - y) + b.(x - y)

= (x - y).(a + b)

l)

5ax - 5ay + bx - by

= 5a.(x - y) + b.(x - y)

= (x - y).(5a + b)

m)

x² + 5x + ax + 5a

= x.(x + 5) + a.(x + 5)

= (x + 5).(x + a)

n)

6a² + 2ab - 3ac - bc

= 2a.(3a + b) - c.(3a + b)

= (3a + b).(2a - c)

o)

t³ + t² - 7t - 7

= t².(t + 1) - 7.(t - 1)

= (t + 1).(t² - 7)

p)

x⁴ - x³ - 9x + 9

= x⁴.(x - 1) - 9.(x - 1)

= (x - 1).(x⁴ - 9)

= (x - 1).[(x²)² - 3²]

= (x - 1).(x² - 3).(x² + 3)

q)

2b² + 2 - b²k - k

= 2.(b² + 1) - k.(b² + 1)

= (b² + 1).(2 - k)

r)

bx² - 2by + 5x² - 10y

= b.(x² - 2y) + 5.(x² - 2y)

= (x² - 2y).(b + 5)

s)

a⁵ + a³ + 2a² + 2

= a³.(a² + 1) + 2.(a² + 1)

= (a² + 1).(a³ + 1)

t)

cx + x + c + 1

= x.(c + 1) + 1.(c + 1)

= (c + 1).(x + 1)

Answer 2

Resposta:

a) ab - b + 2a - 2 =b.(a - 1) + 2.(a - 1) = (a - 1).(b + 2)

                           

b) x6 + 2x4 + ax² + 2a = x⁴.(x² + 2) + a.(x² + 2) = (x² + 2).(x⁴ + a)  

                 

c) by² - 2b + cy² - 2c =b.(y² - 2) + c.(y² - 2) = (y² - 2).(b + c)

           

d)x³ - 10x² + xy - 10y =x².(x - 10) + y.(x - 10) = (x - 10).(x² + y)  

                   

e) 5c + 5 - ac - a =5.(c + 1) - a.(c + 1) = (c + 1).(5 - a)

           

f) am + bm + an + bn =m.(a + b) + n.(a + b) = (a + b).(m + n)

g) ax + 5x + ay + 5y = x.(a + 5) + y.(a + 5)  = (a + 5).(x + y)

h) a³ - a² + a – 1 =a².(a - 1) + 1.(a - 1) = (a - 1).(a² + 1)

 

i)10a³b - 5ab³ + 6a² - 3b² =5ab.(2a² - b²) + 3.(2a² - b²) = (2a² - b²).(5ab + 3)

j) 3a - 6y + ab - 2by =3.(a - 2y) + b.(a - 2y) = (a - 2y).(3 + b)