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x^2-6x+7

Step-by-step explanation:

You can use synthetic division since you are dividing by a linear factor with leading coefficient 1.  (You can also do synthetic division when dividing by a linear factor whose leading coefficient is not 1 but it is a bit trickier.)

So since we are dividing by x-2, 2 goes on the outside.

(If we were dividing by x+2, -2 would go on the outside.)

Now the thing that goes on top inside is the dividend, the numerator which is 1x^3-8x^2+19x-14. If you were missing any terms you would have to place a zero but we aren't. All exponents between 3 and 0 (inclusive meaning to include the 3 and the constant term) on variable x is accounted for.  

2|  1   -8    19     -14

 |       2    -12      14

     1  -6     7       0

So the remainder is 0 and the quotient is x^2-6x+7.

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step-by-step explanation:

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