Question

Divide :

(x
³-6x²+11x-6) / (x²-5x+6)​

Answer 1

step by step expainon:

Divide  

x3 − 6 x 2 + 11 x − 6  by  x − 1 .  

First, you let the coefficients of each degree to be used in the division ( 1 , − 6 , 11 , − 6 ).  

Then, dividing by  x − 1

implies that you use  1  in your upper left. So, put  1 , then a line (I've used a double line), and then write    1   -6  11  -6   to the right.  1  ∣ ∣   1 -6 11  -6  +

First, bring the first  1  down to the bottom, and multiply it by the  1 . Put that  1  below the  - 6 .

1  ∣ ∣  1   -6  11  -6  +  1 − − − − −    1

Then add  

− 6 + 1 = − 5

Put that under the  1 1  ∣ ∣   1  -6  11 -6  + 1 − −− − −  1  -5

Multiply  

1 × − 5 = − 5  and put the  − 5  under the  11 . Then add:  

1  ∣ ∣  1   -6  11  -6  +  1  -5 − − − − − − −− 1   -5   6

Now

1× 6 = 6 , so we put  6  under  − 6  and add::

1  ∣ ∣    1  -6    11   -6  +  1   -5   6 − − − − − −− −  1   -5  6  ∣ 0  

The bottom row ignoring the last number gives us the coefficients of the quotient.

The last number on the bottom row is the remainder (and it is also  

P ( 1 ) ).

So the division gives us:  x 3 − 6 x 2 + 11x − 6 x − 1 =x 2 − 5 x + 6

You can check the answer by multiplyg:

( x − 1 ) ( x 2 -5 x + 6 )  to make sure we get  x 3 −6 x 2 + 11 x − 6 .

Answer 2

Answer:

x - 1

Step-by-step explanation: