Question

x³-6x²+11x-6/x-2 solve it please ​

Answer 1

EXPLANATION.

⇒ x³ - 6x² + 11x - 6/x - 2.

As we know that,

Firstly, put the value of x = 1 in the equation.

⇒ f(1) = (1)³ - 6(1)² + 11(1) - 6.

⇒ f(1) = 1 - 6 + 11 - 6.

⇒ f(1) = 12 - 12.

⇒ f(1) = 0.

As we can see that,

⇒ (x - 1) is a factor of f(x).

Divide x³ - 6x² + 11x - 6 by (x - 1).

We get,

⇒ x² - 5x + 6.

We can write as,

⇒ (x - 1)(x² - 5x + 6).

⇒ x² - 5x + 6.

Factorizes the equation into middle term splits, we get.

⇒ x² - 3x - 2x + 6.

⇒ x(x - 3) - 2(x - 3).

⇒ (x - 2)(x - 3).

⇒ (x - 1)(x - 2)(x - 3).

The original equation :

⇒ (x - 1)(x - 2)(x - 3)/(x - 2).

⇒ (x - 1)(x - 3).

⇒ x² - 3x - x + 3.

⇒ x² - 4x + 3.

Answer 2

Answer:

Given Question :

$\sf \frac{x³-6x²+11x-6}{x - 2}$

Required Answer :

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

Using the rational root therom

$\sf \: = \frac{(x - 1) \frac{ {x}^{3} - {6x }^{2} + 11x - 6 }{x - 1} }{x - 2}$

$\sf \frac{x³ - 6x² + 11x - 6}{x - 1} = {x}^{2} - 5x + 6$

$\sf= \frac{(x - 1)( {x}^{2} - 5x + 6) }{x - 2}$

$\sf \: factor \: x²-5x+6:(x-2)(x-3)$

$\sf = \frac{(x-1)(x-2)(x-3)}{x - 2}$

Now , Cancelling common factor : x - 2

$\sf = (x-1)(x-3)$