Question

Calcule o MMC de cada item abaixo:

a) x2 + 2x + 1 ; 3x + 3

b) 9x - 6x2 + x3 ; 5x2 - 45

c) x2 - 1 ; x2 + xa + x + a

Answer 1

Explicação passo-a-passo:

a)

• x² + 2x + 1 = (x + 1)²

• 3x + 3 = 3.(x + 1)

O mmc é:

mmc = 3.(x + 1)²

mmc = 3.(x² + 2x + 1)

mmc = 3x² + 6x + 3

b)

• 9x - 6x² + x³ = x.(9 - 6x + x²) = x.(x - 3)²

• 5x² - 45 = 5.(x² - 9) = 5.(x - 3).(x + 3)

O mmc é:

mmc = 3.5.x.(x - 3)².(x + 3)

mmc = 15.x.(x² - 6x + 9).(x + 3)

mmc = 15x.(x³ - 6x² + 9x + 3x² - 18x + 27)

mmc = 15x.(x³ - 3x² - 9x + 27)

mmc = 15x⁴ - 45x³ - 135x² + 405

c)

• x² - 1 = (x + 1).(x - 1)

• x² + xa + x + a

= x.(x + a) + 1.(x + a)

= (x + a).(x + 1)

O mmc é:

mmc = (x + 1).(x - 1).(x + a)

mmc = (x² - 1).(x + a)

mmc = x³ - x + ax² - a

mmc = x³ + ax² - x - a