Question

Calcule os quocientes:
a) ( x² + 5x + 6) : (x + 2)
b) (x² - 7x + 10 ) : ( x - 2)
c) (2x² + 6x + 4 ) : ( x + 1)
d) ( x³ - 6x² + 11x – 6) : ( x – 3)

Answer 1

Explicação passo-a-passo:

a) x² + 5x + 6 | x + 2

-x² - 2x x + 3

-------------------

3x + 6

- 3x - 6

-----------

(0)

b) x² - 7x + 10 | x - 2

-x² + 2x x - 5

-------------------

-5x + 10

+5x - 10

------------

(0)

c) 2x² + 6x + 4 | x + 1

-2x² - 2x 2x + 4

-------------------

4x + 4

-4x - 4

----------

(0)

d) x³ - 6x² + 11x - 6 | x - 3

-x³ + 3x² x² - 3x + 2

-------------------------

-3x² + 11x - 6

+3x² - 9x

-----------------

2x - 6

-2x + 6

----------

(0)

Answer 2

Oie, Td Bom?!

a)

$(x {}^{2} + 5x + 6) \div (x + 2)$

$\frac{x {}^{2} + 5x + 6}{x + 2}$

$\frac{x {}^{2} + 3x + 2x + 6 }{x + 2}$

$\frac{x \: . \: (x + 3) + 2(x + 3)}{x + 2}$

$\frac{(x + 3) \: . \: (x + 2)}{x + 2}$

$x + 3$

b)

$(x {}^{2} - 7x + 10) \div (x - 2)$

$\frac{x {}^{2} - 7x + 10}{x - 2}$

$\frac{x {}^{2} - 2x - 5x + 10}{x - 2}$

$\frac{x \: . \: (x - 2) - 5(x - 2)}{x - 2}$

$\frac{(x - 2) \: . \: (x - 5)}{x - 2}$

$x - 5$

c)

$(2x {}^{2} + 6x + 4) \div (x + 1)$

$\frac{2x {}^{2} + 6x + 4 }{x + 1}$

$\frac{2(x {}^{2} + 3x + 2) }{x + 1}$

$\frac{2(x {}^{2} + 2x + x + 2)}{x + 1}$

$\frac{2(x \: . \: (x + 2) + x + 2)}{x + 1}$

$\frac{2(x + 2) \: . \: (x + 1)}{x + 1}$

$2(x + 2)$

$2x + 4$

d)

$(x {}^{3} - 6 x{}^{2} + 11x - 6) \div (x - 3)$

$\frac{x {}^{3} - 6x {}^{2} + 11x - 6 }{x - 3}$

$\frac{x {}^{3} - x {}^{2} - 5x {}^{2} + 5x + 6x - 6 }{x - 3}$

$\frac{x {}^{2} \: . \: (x - 1) - 5x \: . \: (x - 1) + 6(x - 1) }{x - 3}$

$\frac{(x - 1) \: . \: (x {}^{2} - 5x + 6)}{x - 3}$

$\frac{(x - 1) \: . \: (x {}^{2} - 2x - 3x + 6)}{x - 3}$

$\frac{(x - 1) \: . \: (x \: . \: (x - 2) - 3(x - 2))}{x - 3}$

$\frac{(x - 1) \: . \: (x - 2) \: . \: (x - 3)}{x - 3}$

$(x - 1) \: . \: (x - 2)$

$x {}^{2} - 2x - x + 2$

$x {}^{2} - 3x + 2$

Att. Makaveli1996