Question

What is the result when 2x^3 -9x^2 +11x-6 is divided by x-3 @Michele_Laino

Answer 1

3 I   2    -9    11   -6
   I   
   I   2     6    -9     6
    ------------------------
       2    -3     2     0

2x² - 3x + 2 is the answer

Answer 2

2x^2 - 3x + 2  
I hope that the formatting isn't destroyed since this is an exercise in long division of polynomials. We have:
 (2x^3 - 9x^2 + 11x - 6)/(x-3) 
 Look at the highest term in the numerator which is 2x^3. Now divide by the highest term in the divisor which is x. Perform that division, so 2x^3/x = 2x^2. And finally, multiply the divisor by the quotient term you just made and then subtract that from the numerator. So we have
 Partial quotient = 2x^3/x = 2x^2
 Multiply the divisor = (x-3)*2x^2 = 2x^3 - 6x^2
 Subtract from numerator = (2x^3 - 9x^2 + 11x - 6) - (2x^3 - 6x^2)
 = (- 9x^2 + 11x - 6) + 6x^2
 = (- 3x^2 + 11x - 6) 
 So we now have a quotient of 2x^2 and a simpler problem of
 (- 3x^2 + 11x - 6)/(x-3). Let's continue. 
 Partial quotient = -3x^2/x = -3x
 Multiply the divisor = -3x(x-3) = -3x^2 + 9x
 Subtract from numerator = (- 3x^2 + 11x - 6) - (-3x^2 + 9x)
 = (11x - 6) - 9x
 = 2x - 6 
 And our quotient so far is now 2x^2 - 3x, and the simpler problem is: (2x -
6)/(x - 3). So let's continue:
 Partial quotient = 2x/x = 2
 Multiply the divisor = 2(x-3) = 2x - 6
 Subtract from numerator = (2x - 6) - (2x - 6) = 0 
 And we're done with the quotient of 2x^2 - 3x + 2